The Scientific World Journal: Mathematical Analysis
http://www.hindawi.com
The latest articles from Hindawi Publishing Corporation
© 2014 , Hindawi Publishing Corporation . All rights reserved.

The Asymptotic Solutions for a Class of Nonlinear Singular Perturbed Differential Systems with Time delays
Wed, 16 Apr 2014 16:12:57 +0000
http://www.hindawi.com/journals/tswj/2014/965376/
We study a kind of vector singular perturbed delaydifferential equations. By using the methods of boundary function and fractional steps, we construct the formula of asymptotic expansion and confirm the interior layer at . Meanwhile, on the basis of functional analysis skill, the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved.
Han Xu and Yinlai Jin
Copyright © 2014 Han Xu and Yinlai Jin. All rights reserved.

Bifurcations of Nontwisted Heteroclinic Loop with Resonant Eigenvalues
Wed, 16 Apr 2014 09:36:17 +0000
http://www.hindawi.com/journals/tswj/2014/716082/
By using the foundational solutions of the linear variational equation of the unperturbed system along the heteroclinic orbits to establish the local
coordinate systems in the small tubular neighborhoods of the
heteroclinic orbits, we study the bifurcation problems of
nontwisted heteroclinic loop with resonant eigenvalues. The
existence, numbers, and existence regions of 1heteroclinic loop,
1homoclinic loop, 1periodic orbit, 2fold 1periodic orbit, and two
1periodic orbits are obtained. Meanwhile, we give the
corresponding bifurcation surfaces.
Yinlai Jin, Xiaowei Zhu, Zheng Guo, Han Xu, Liqun Zhang, and Benyan Ding
Copyright © 2014 Yinlai Jin et al. All rights reserved.

Determination of Coefficients of HighOrder Schemes for RiemannLiouville Derivative
Tue, 15 Apr 2014 13:02:29 +0000
http://www.hindawi.com/journals/tswj/2014/402373/
Although there have existed some numerical algorithms for the fractional differential equations, developing highorder methods (i.e., with convergence
order greater than or equal to 2) is just the beginning. Lubich has ever proposed
the highorder schemes when he studied the fractional linear multistep
methods, where he constructed the th order schemes for
the th order RiemannLiouville integral and th order RiemannLiouville derivative. In this paper, we study such a problem and develop recursion
formulas to compute these coefficients in the higherorder schemes. The coefficients
of higherorder schemes are also obtained. We first find that these coefficients are oscillatory, which is similar to Runge’s phenomenon. So, they are not suitable for numerical calculations. Finally, several numerical examples are implemented to testify the efficiency of the numerical schemes for .
Rifang Wu, Hengfei Ding, and Changpin Li
Copyright © 2014 Rifang Wu et al. All rights reserved.

On Fourier Series of FuzzyValued Functions
Thu, 10 Apr 2014 12:46:20 +0000
http://www.hindawi.com/journals/tswj/2014/782652/
Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering. In the present paper since the utilization of Zadeh’s Extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct a fuzzyvalued function on a closed interval via related membership function. We derive uniform convergence of a fuzzyvalued function sequences and series with level sets. Also we study Hukuhara differentiation and Henstock integration of a fuzzyvalued function with some necessary inclusions. Furthermore, Fourier series of periodic fuzzyvalued functions is defined and its complex form is given via sine and cosine fuzzy coefficients with an illustrative example. Finally, by using the Dirichlet kernel and its properties, we especially examine the convergence of Fourier series of fuzzyvalued functions at each point of discontinuity, where onesided limits exist.
Uğur Kadak and Feyzi Başar
Copyright © 2014 Uğur Kadak and Feyzi Başar. All rights reserved.

Implementation of Steiner Point of Fuzzy Set
Wed, 09 Apr 2014 12:01:44 +0000
http://www.hindawi.com/journals/tswj/2014/593065/
This paper deals with the implementation of Steiner point of fuzzy set. Some definitions and properties of Steiner point are investigated and extended to fuzzy set. This paper focuses on establishing efficient methods to compute Steiner point of fuzzy set. Two strategies of computing Steiner point of fuzzy set are proposed. One is called linear combination of Steiner points computed by a series of crisp αcut sets of the fuzzy set. The other is an approximate method, which is trying to find the optimal αcut set approaching the fuzzy set. Stability analysis of Steiner point of fuzzy set is also studied. Some experiments on image processing are given, in which the two methods are applied for implementing Steiner point of fuzzy image, and both strategies show their own advantages in computing Steiner point of fuzzy set.
Jiuzhen Liang and Dejiang Wang
Copyright © 2014 Jiuzhen Liang and Dejiang Wang. All rights reserved.

Global Existence and Energy Decay Rates for a KirchhoffType Wave Equation with Nonlinear Dissipation
Mon, 07 Apr 2014 09:49:53 +0000
http://www.hindawi.com/journals/tswj/2014/716740/
The first objective of this paper is to prove the existence and uniqueness of
global solutions for a Kirchhofftype wave equation with nonlinear dissipation
of the form under suitable assumptions on , and . Next, we derive decay estimates of the energy under some growth conditions on the nonlinear dissipation . Lastly, numerical simulations in order to verify the analytical results are given.
Daewook Kim, Dojin Kim, KeumShik Hong, and Il Hyo Jung
Copyright © 2014 Daewook Kim et al. All rights reserved.

Leapfrog/Finite Element Method for Fractional Diffusion Equation
Thu, 03 Apr 2014 13:43:57 +0000
http://www.hindawi.com/journals/tswj/2014/982413/
We analyze a fully discrete leapfrog/Galerkin finite
element method for the numerical solution of the space fractional order (fractional for simplicity) diffusion equation. The generalized fractional derivative spaces are
defined in a bounded interval. And some related properties are further discussed for the
following finite element analysis. Then the fractional diffusion equation
is discretized in space by the finite element method and in time by the explicit
leapfrog scheme. For the resulting fully discrete, conditionally stable scheme,
we prove an error bound of finite element accuracy and of second order in
time. Numerical examples are included to confirm our theoretical analysis.
Zhengang Zhao and Yunying Zheng
Copyright © 2014 Zhengang Zhao and Yunying Zheng. All rights reserved.

Limit of Riemann Solutions to the Nonsymmetric System of KeyfitzKranzer Type
Thu, 03 Apr 2014 09:37:17 +0000
http://www.hindawi.com/journals/tswj/2014/287256/
The limit of Riemann solutions to the nonsymmetric system of KeyfitzKranzer type with a scaled pressure is considered for both polytropic gas and generalized Chaplygin gas. In the former case, the delta shock wave can be obtained as the limit of shock wave and contact discontinuity when and the parameter tends to zero. The point is, the delta shock wave is not the one of transport equations, which is obviously different from cases of some other systems such as Euler equations or relativistic Euler equations. For the generalized Chaplygin gas, unlike the polytropic or isothermal gas, there exists a certain critical value depending only on the Riemann initial data, such that when drops to , the delta shock wave appears as , which is actually a delta solution of the same system in one critical case. Then as becomes smaller and goes to zero at last, the delta shock wave solution is the exact one of transport equations. Furthermore, the vacuum states and contact discontinuities can be obtained as the limit of Riemann solutions when and , respectively.
Lihui Guo and Gan Yin
Copyright © 2014 Lihui Guo and Gan Yin. All rights reserved.

Monotone Data Visualization Using Rational Trigonometric Spline Interpolation
Thu, 03 Apr 2014 09:35:38 +0000
http://www.hindawi.com/journals/tswj/2014/602453/
Rational cubic and bicubic trigonometric schemes are developed to conserve monotonicity of curve and surface data, respectively. The rational cubic function has four parameters in each subinterval, while the rational bicubic partially blended function has eight parameters in each rectangular patch. The monotonicity of curve and surface data is retained by developing constraints on some of these parameters in description of rational cubic and bicubic trigonometric functions. The remaining parameters are kept free to modify the shape of curve and surface if required. The developed algorithm is verified mathematically and demonstrated graphically.
Farheen Ibraheem, Maria Hussain, and Malik Zawwar Hussain
Copyright © 2014 Farheen Ibraheem et al. All rights reserved.

Anticontrol of Hopf Bifurcation and Control of Chaos for a Finance System through Washout Filters with Time Delay
Thu, 03 Apr 2014 09:29:51 +0000
http://www.hindawi.com/journals/tswj/2014/983034/
A controlled model for a financial system through washoutfilteraided dynamical feedback control laws is developed, the problem of anticontrol of Hopf bifurcation from the steady state is studied, and the existence, stability, and direction of bifurcated periodic solutions are discussed in detail. The obtained results show that the delay on price index has great influences on the financial system, which can be applied to suppress or avoid the chaos phenomenon appearing in the financial system.
Huitao Zhao, Mengxia Lu, and Junmei Zuo
Copyright © 2014 Huitao Zhao et al. All rights reserved.

Two Different Methods for Numerical Solution of the Modified Burgers’ Equation
Thu, 03 Apr 2014 08:56:09 +0000
http://www.hindawi.com/journals/tswj/2014/780269/
A numerical solution of the modified Burgers’ equation (MBE) is obtained by
using quartic Bspline subdomain finite element method (SFEM) over which the nonlinear term is locally linearized and using quartic Bspline differential quadrature (QBDQM) method. The accuracy and efficiency of the methods are discussed by
computing and error norms. Comparisons are made with those of some earlier papers. The obtained numerical results show that the methods are effective numerical schemes to solve the MBE. A linear stability analysis, based on the von Neumann scheme, shows the SFEM is unconditionally stable. A rate of convergence analysis
is also given for the DQM.
Seydi Battal Gazi Karakoç, Ali Başhan, and Turabi Geyikli
Copyright © 2014 Seydi Battal Gazi Karakoç et al. All rights reserved.

SincChebyshev Collocation Method for a Class of Fractional DiffusionWave Equations
Tue, 01 Apr 2014 08:16:23 +0000
http://www.hindawi.com/journals/tswj/2014/143983/
This paper is devoted to investigating the numerical solution for a class of fractional diffusionwave equations with a variable coefficient where the fractional derivatives are described in the Caputo sense. The approach is based on the collocation technique where the shifted Chebyshev polynomials in time and the sinc functions in space are utilized, respectively. The problem is reduced to the solution of a system of linear algebraic equations. Through the numerical example, the procedure is tested and the efficiency of the proposed method is confirmed.
Zhi Mao, Aiguo Xiao, Zuguo Yu, and Long Shi
Copyright © 2014 Zhi Mao et al. All rights reserved.

Diagonally Implicit Symplectic RungeKutta Methods with High Algebraic and Dispersion Order
Tue, 01 Apr 2014 06:42:02 +0000
http://www.hindawi.com/journals/tswj/2014/147801/
The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper. A diagonally implicit symplectic ninestages RungeKutta method with algebraic order 6 and dispersion order 8 is presented. Numerical experiments with some Hamiltonian oscillatory problems are presented to show the proposed method is as competitive as the existing same type RungeKutta methods.
Y. H. Cong and C. X. Jiang
Copyright © 2014 Y. H. Cong and C. X. Jiang. All rights reserved.

Recent Progress on Nonlinear Schrödinger Systems with Quadratic Interactions
Mon, 31 Mar 2014 14:01:31 +0000
http://www.hindawi.com/journals/tswj/2014/214821/
The study of nonlinear Schrödinger systems with quadratic interactions has attracted much attention in the recent years. In this paper, we summarize time decay estimates of small solutions to the systems under the mass resonance condition in 2dimensional space. We show the existence of wave operators and modified wave operators of the systems under some mass conditions in dimensional space, where . The existence of scattering operators and finite time blowup of the solutions for the systems in higher space dimensions is also shown.
Chunhua Li and Nakao Hayashi
Copyright © 2014 Chunhua Li and Nakao Hayashi. All rights reserved.

On the Limit Cycles of a Class of Planar Singular Perturbed Differential Equations
Mon, 31 Mar 2014 00:00:00 +0000
http://www.hindawi.com/journals/tswj/2014/379897/
Relaxation oscillations of twodimensional planar singular perturbed systems with a layer equation exhibiting canard cycles are studied. The canard cycles under consideration contain two turning points and two jump points. We suppose that there exist three parameters permitting generic breaking at both the turning points and the connecting fast orbit. The conditions of one (resp., two, three) relaxation oscillation near the canard cycles are given by studying a map from the space of phase parameters to the space of breaking parameters.
Yuhai Wu and Jingjing Zhou
Copyright © 2014 Yuhai Wu and Jingjing Zhou. All rights reserved.

Blowup Phenomena for the Compressible Euler and EulerPoisson Equations with Initial Functional Conditions
Sun, 30 Mar 2014 11:40:54 +0000
http://www.hindawi.com/journals/tswj/2014/580871/
We study, in the radial symmetric case, the finite time life span of the compressible Euler or EulerPoisson equations in . For time , we can define a functional associated with the solution of the equations and some testing function . When the pressure function of the governing equations is of the form , where is the density function, is a constant, and , we can show that the nontrivial solutions with nonslip boundary condition will blow up in finite time if satisfies some initial functional conditions defined by the integrals of . Examples of the testing functions include , , , , and . The corresponding blowup result for the 1dimensional nonradial symmetric case is also given.
Sen Wong and Manwai Yuen
Copyright © 2014 Sen Wong and Manwai Yuen. All rights reserved.

Discontinuous Mixed Covolume Methods for Parabolic Problems
Sun, 30 Mar 2014 08:51:28 +0000
http://www.hindawi.com/journals/tswj/2014/867863/
We present the semidiscrete and the backward Euler fully discrete discontinuous mixed covolume schemes for parabolic problems on triangular meshes. We give the error analysis of the discontinuous mixed covolume schemes and obtain optimal order error estimates in discontinuous and firstorder error estimate in .
Ailing Zhu and Ziwen Jiang
Copyright © 2014 Ailing Zhu and Ziwen Jiang. All rights reserved.

Fixed Points of Contractive Mappings in MetricLike Spaces
Sun, 30 Mar 2014 07:44:55 +0000
http://www.hindawi.com/journals/tswj/2014/471827/
We discuss topological structure of metriclike spaces and demonstrate a fundamental lemma for the convergence of sequences. As an application we prove certain fixed point results in the setup of such spaces for different types of contractive mappings. Finally, some periodic point results in metriclike spaces are obtained. Two examples are presented in order to verify the effectiveness and applicability of our main results.
Nawab Hussain, Jamal Rezaei Roshan, Vahid Parvaneh, and Zoran Kadelburg
Copyright © 2014 Nawab Hussain et al. All rights reserved.

A Time Delay PredatorPrey System with ThreeStageStructure
Thu, 27 Mar 2014 07:19:14 +0000
http://www.hindawi.com/journals/tswj/2014/512838/
A predatorprey system was studied that has a discrete delay, stagestructure, and BeddingtonDeAngelis functional response, where predator species has three stages, immature, mature, and old age stages. By using of Mawhin's continuous theorem of coincidence degree theory, a sufficient condition is obtained for the existence of a positive periodic solution.
Qiaoqin Gao and Zhen Jin
Copyright © 2014 Qiaoqin Gao and Zhen Jin. All rights reserved.

The Existence of Periodic Orbits and Invariant Tori for Some 3Dimensional Quadratic Systems
Wed, 26 Mar 2014 08:02:41 +0000
http://www.hindawi.com/journals/tswj/2014/705703/
We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in LotkaVolterra systems and the existence of invariant tori in quadratic systems in .
Yanan Jiang, Maoan Han, and Dongmei Xiao
Copyright © 2014 Yanan Jiang et al. All rights reserved.

An Analysis on Local Convergence of Inexact NewtonGauss Method for Solving Singular Systems of Equations
Wed, 26 Mar 2014 00:00:00 +0000
http://www.hindawi.com/journals/tswj/2014/752673/
We study the local convergence properties of inexact NewtonGauss method for singular systems of equations. Unified estimates of radius of convergence balls for one kind of singular systems of equations with constant rank derivatives are obtained. Application to the Smale point estimate theory is provided and some important known results are extended and/or improved.
Fangqin Zhou
Copyright © 2014 Fangqin Zhou. All rights reserved.

Upper Semicontinuity of Pullback Attractors for the 3D Nonautonomous BenjaminBonaMahony Equations
Wed, 26 Mar 2014 00:00:00 +0000
http://www.hindawi.com/journals/tswj/2014/853139/
We will study the upper semicontinuity of
pullback attractors for the 3D nonautonomouss BenjaminBonaMahony
equations with external force perturbation terms. Under some regular assumptions, we can prove the pullback attractors
of equation , converge to the global
attractor of the abovementioned equation with
for any .
Xinguang Yang, Xiaosong Wang, Juntao Li, and Lingrui Zhang
Copyright © 2014 Xinguang Yang et al. All rights reserved.

Bifurcation Analysis in Models for VectorBorne Diseases with Logistic Growth
Tue, 25 Mar 2014 12:00:50 +0000
http://www.hindawi.com/journals/tswj/2014/195864/
We establish and study vectorborne models with logistic and exponential growth of vector and host populations, respectively. We discuss and analyses the existence and stability of equilibria. The model has backward bifurcation and may have no, one, or two positive equilibria when the basic reproduction number is less than one and one, two, or three endemic equilibria when is greater than one under different conditions. Furthermore, we prove that the diseasefree equilibrium is stable if is less than 1, it is unstable otherwise. At last, by numerical simulation, we find rich dynamical behaviors in the model. By taking the natural death rate of host population as a bifurcation parameter, we find that the system may undergo a backward bifurcation, saddlenode bifurcation, Hopf bifurcation, BogdanovTakens bifurcation, and cusp bifurcation with the saturation parameter varying. The natural death rate of host population is a crucial parameter. If the natural death rate is higher, then the host population and the disease will die out. If it is smaller, then the host and vector population will coexist. If it is middle, the period solution will occur. Thus, with the parameter varying, the disease will spread, occur periodically, and finally become extinct.
Guihua Li and Zhen Jin
Copyright © 2014 Guihua Li and Zhen Jin. All rights reserved.

Numerical Modeling of the Photothermal Processing for Bubble Forming around Nanowire in a Liquid
Mon, 24 Mar 2014 12:20:29 +0000
http://www.hindawi.com/journals/tswj/2014/794630/
An accurate computation of the temperature is an important factor in determining the shape of a bubble around a nanowire immersed in a liquid. The study of the physical phenomenon consists in solving a photothermic coupled problem between light and nanowire. The numerical multiphysic model is used to study the variations of the temperature and the shape of the created bubble by illumination of the nanowire. The optimization process, including an adaptive remeshing scheme, is used to solve the problem through a finite element method. The study of the shape evolution of the bubble is made taking into account the physical and geometrical parameters of the nanowire. The relation between the sizes and shapes of the bubble and nanowire is deduced.
Anis Chaari, Laurence GiraudMoreau, Thomas Grosges, and Dominique Barchiesi
Copyright © 2014 Anis Chaari et al. All rights reserved.

Bifurcations of Orbit and Inclination Flips Heteroclinic Loop with Nonhyperbolic Equilibria
Sun, 23 Mar 2014 13:05:40 +0000
http://www.hindawi.com/journals/tswj/2014/585609/
The bifurcations of
heteroclinic loop with one nonhyperbolic equilibrium and one
hyperbolic saddle are considered, where the nonhyperbolic
equilibrium is supposed to undergo a transcritical bifurcation;
moreover, the heteroclinic loop has an orbit flip and an inclination
flip. When the nonhyperbolic equilibrium does not undergo a
transcritical bifurcation, we establish the coexistence and
noncoexistence of the periodic orbits and homoclinic orbits. While
the nonhyperbolic equilibrium undergoes the transcritical
bifurcation, we obtain the noncoexistence of the periodic orbits and
homoclinic orbits and the existence of two or three heteroclinic
orbits.
Fengjie Geng and Junfang Zhao
Copyright © 2014 Fengjie Geng and Junfang Zhao. All rights reserved.

Existence and Uniqueness Theorems for Impulsive Fractional Differential Equations with the TwoPoint and Integral Boundary Conditions
Sun, 23 Mar 2014 00:00:00 +0000
http://www.hindawi.com/journals/tswj/2014/918730/
We study a boundary value problem for the system of nonlinear impulsive fractional differential equations of order involving the twopoint and integral boundary conditions. Some new results on existence and uniqueness of a solution are established by using fixed point theorems. Some illustrative examples are also presented. We extend previous results even in the integer case .
M. J. Mardanov, N. I. Mahmudov, and Y. A. Sharifov
Copyright © 2014 M. J. Mardanov et al. All rights reserved.

A Maximal Element Theorem in FWCSpaces and Its Applications
Thu, 20 Mar 2014 09:11:18 +0000
http://www.hindawi.com/journals/tswj/2014/890696/
A maximal element theorem is proved in finite weakly convex spaces (FWCspaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWCspaces. The results represented in this paper unify and extend some known results in the literature.
Haishu Lu, Qingwen Hu, and Yulin Miao
Copyright © 2014 Haishu Lu et al. All rights reserved.

MeanVariance Portfolio Selection for DefinedContribution Pension Funds with Stochastic Salary
Thu, 20 Mar 2014 07:17:04 +0000
http://www.hindawi.com/journals/tswj/2014/826125/
This paper focuses on a continuoustime dynamic meanvariance portfolio selection problem of definedcontribution pension funds with stochastic salary, whose risk comes from both financial market and nonfinancial market. By constructing a special Riccati equation as a continuous (actually a viscosity) solution to the HJB equation, we obtain an explicit closed form solution for the optimal investment portfolio as well as the efficient frontier.
Chubing Zhang
Copyright © 2014 Chubing Zhang. All rights reserved.

On the Shape of Limit Cycles That Bifurcate from Isochronous Center
Wed, 19 Mar 2014 14:18:03 +0000
http://www.hindawi.com/journals/tswj/2014/320406/
New idea and algorithm are proposed to compute asymptotic expression of limit cycles bifurcated from the isochronous center. Compared with known inverse integrating factor method, new algorithm to analytically computing shape of limit cycle proposed in this paper is simple and easy to apply. The applications of new algorithm to some examples are also given.
Guang Chen and Yuhai Wu
Copyright © 2014 Guang Chen and Yuhai Wu. All rights reserved.

Dynamic Properties of the Solow Model with Bounded Technological Progress and TimetoBuild Technology
Wed, 19 Mar 2014 13:44:04 +0000
http://www.hindawi.com/journals/tswj/2014/908629/
We introduce a timetobuild technology in a Solow model with bounded technological progress. Our analysis shows that the system may be asymptotically stable, or it can produce stability switches and Hopf bifurcations when time delay varies. The direction and the stability criteria of the bifurcating periodic solutions are obtained by the normal form theory and the center manifold theorem. Numerical simulations confirms the theoretical results.
Luca Guerrini and Mauro Sodini
Copyright © 2014 Luca Guerrini and Mauro Sodini. All rights reserved.

A Domain Decomposition Method for Time Fractional ReactionDiffusion Equation
Wed, 19 Mar 2014 09:01:53 +0000
http://www.hindawi.com/journals/tswj/2014/681707/
The computational complexity of onedimensional time fractional reactiondiffusion equation is compared with for classical integer reactiondiffusion equation. Parallel computing is used to overcome this challenge. Domain decomposition method (DDM) embodies large potential for parallelization of the numerical solution for fractional equations and serves as a basis for distributed, parallel computations. A domain decomposition algorithm for time fractional reactiondiffusion equation with implicit finite difference method is proposed. The domain decomposition algorithm keeps the same parallelism but needs much fewer iterations, compared with Jacobi iteration in each time step. Numerical experiments are used to verify the efficiency of the obtained algorithm.
Chunye Gong, Weimin Bao, Guojian Tang, Yuewen Jiang, and Jie Liu
Copyright © 2014 Chunye Gong et al. All rights reserved.

On HardyPachpatteCopson's Inequalities
Tue, 18 Mar 2014 07:08:21 +0000
http://www.hindawi.com/journals/tswj/2014/607347/
We establish new inequalities similar to HardyPachpatteCopson’s type inequalities. These results in special cases yield some of the recent results.
ChangJian Zhao and WingSum Cheung
Copyright © 2014 ChangJian Zhao and WingSum Cheung. All rights reserved.

A Note on the Solutions of Some Nonlinear Equations Arising in ThirdGrade Fluid Flows: An Exact Approach
Mon, 17 Mar 2014 08:26:34 +0000
http://www.hindawi.com/journals/tswj/2014/109128/
In this communication, we utilize some basic symmetry
reductions to transform the governing nonlinear partial differential
equations arising in the study of thirdgrade fluid flows into ordinary
differential equations. We obtain some simple closedform steadystate
solutions of these reduced equations. Our solutions are valid for the whole
domain [0,∞) and also satisfy the physical boundary conditions. We
also present the numerical solutions for some of the underlying equations.
The graphs corresponding to the essential physical parameters of the flow
are presented and discussed.
Taha Aziz and F. M. Mahomed
Copyright © 2014 Taha Aziz and F. M. Mahomed. All rights reserved.

A Novel Iterative Scheme and Its Application to Differential Equations
Sun, 16 Mar 2014 12:46:14 +0000
http://www.hindawi.com/journals/tswj/2014/605376/
The purpose of this paper is to employ an alternative approach to reconstruct the standard variational iteration algorithm II proposed by He, including Lagrange multiplier, and to give a simpler formulation of Adomian decomposition and modified Adomian decomposition method in terms of newly proposed variational iteration methodII (VIM). Through careful investigation of the earlier variational iteration algorithm and Adomian decomposition method, we find unnecessary calculations for Lagrange multiplier and also repeated calculations involved in each iteration, respectively. Several examples are given to verify the reliability and efficiency of the method.
Yasir Khan, F. Naeem, and Zdeněk Šmarda
Copyright © 2014 Yasir Khan et al. All rights reserved.

Some Refinements and Generalizations of I. Schur Type Inequalities
Sun, 16 Mar 2014 11:23:21 +0000
http://www.hindawi.com/journals/tswj/2014/709358/
Recently, extensive researches on estimating the value of e have been studied. In this paper, the structural characteristics of I. Schur type inequalities are exploited to generalize the corresponding inequalities by variable parameter techniques. Some novel upper and lower bounds for the I. Schur inequality have also been obtained and the upper bounds may be obtained with the help of Maple and automated proving package (Bottema). Numerical examples are employed to demonstrate the reliability of the approximation of these new upper and lower bounds, which improve some known results in the recent literature.
XianMing Gu, TingZhu Huang, WeiRu Xu, HouBiao Li, Liang Li, and XiLe Zhao
Copyright © 2014 XianMing Gu et al. All rights reserved.

Anisotropic Hardy Spaces of MusielakOrlicz Type with Applications to Boundedness of Sublinear Operators
Sun, 16 Mar 2014 08:06:43 +0000
http://www.hindawi.com/journals/tswj/2014/306214/
Let be a MusielakOrlicz function and an expansive dilation. In this paper, the authors introduce the anisotropic Hardy space of MusielakOrlicz type, , via the grand maximal function. The authors then obtain some realvariable characterizations of in terms of the radial, the nontangential, and the tangential maximal functions, which generalize the known results on the anisotropic Hardy space with and are new even for its weighted variant. Finally, the authors characterize these spaces by anisotropic atomic decompositions. The authors also obtain the finite atomic decomposition characterization of , and, as an application, the authors prove that, for a given admissible triplet , if is a sublinear operator and maps all atoms with (or all continuous atoms with ) into uniformly bounded elements of some quasiBanach spaces , then uniquely extends to a bounded sublinear operator from to . These results are new even for anisotropic OrliczHardy spaces on .
Baode Li, Dachun Yang, and Wen Yuan
Copyright © 2014 Baode Li et al. All rights reserved.

Nonoscillatory Solutions for System of Neutral Dynamic Equations on Time Scales
Sun, 16 Mar 2014 07:33:49 +0000
http://www.hindawi.com/journals/tswj/2014/768215/
We will discuss nonoscillatory solutions to the dimensional functional system of neutral type dynamic equations on time scales. We will establish some sufficient conditions for nonoscillatory solutions with the property .
Zhanhe Chen, Taixiang Sun, Qi Wang, and Hongjian Xi
Copyright © 2014 Zhanhe Chen et al. All rights reserved.

On the Iterative Methods of Linearization, Decrease of Order and Dimension of the KarmanType PDEs
Sun, 16 Mar 2014 07:12:17 +0000
http://www.hindawi.com/journals/tswj/2014/792829/
Iterative methods to achieve a suitable linearization as well as a decrease of the order and dimension of nonlinear partial differential equations of the eighth order into the biharmonic and Poissontype differential equations with their simultaneous linearization are proposed in this work. Validity and reliability of the obtained results are discussed using computer programs developed by the authors.
A. V. Krysko, J. Awrejcewicz, S. P. Pavlov, M. V. Zhigalov, and V. A. Krysko
Copyright © 2014 A. V. Krysko et al. All rights reserved.

On Ulam's Type Stability of the Cauchy Additive Equation
Sun, 16 Mar 2014 00:00:00 +0000
http://www.hindawi.com/journals/tswj/2014/540164/
We prove a general result on Ulam's type stability of the functional equation , in the class of functions mapping a commutative group into a commutative group. As a consequence, we deduce from it some hyperstability outcomes. Moreover, we also show how to use that result to improve some earlier stability estimations given by Isaac and Rassias.
Janusz Brzdęk
Copyright © 2014 Janusz Brzdęk. All rights reserved.

A Directed Continuous Time Random Walk Model with Jump Length Depending on Waiting Time
Thu, 13 Mar 2014 12:21:34 +0000
http://www.hindawi.com/journals/tswj/2014/182508/
In continuum onedimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the LaplaceLaplace transform of the probability density function of finding the walker at position at time is completely determined by the Laplace transform of the probability density function of the waiting time. In terms of the probability density function of the waiting time in the Laplace domain, the limit distribution of the random process and the corresponding evolving equations are derived.
Long Shi, Zuguo Yu, Zhi Mao, and Aiguo Xiao
Copyright © 2014 Long Shi et al. All rights reserved.

Strong Convergence Theorems for a Common Fixed Point of a Finite Family of Bregman Weak Relativity Nonexpansive Mappings in Reflexive Banach Spaces
Thu, 13 Mar 2014 08:17:18 +0000
http://www.hindawi.com/journals/tswj/2014/493450/
We introduce an iterative process for finding an element of a common fixed point of a finite family of Bregman weak relatively nonexpansive mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.
Habtu Zegeye and Naseer Shahzad
Copyright © 2014 Habtu Zegeye and Naseer Shahzad. All rights reserved.

A Parallel Algorithm for the TwoDimensional Time Fractional Diffusion Equation with Implicit Difference Method
Wed, 12 Mar 2014 12:53:01 +0000
http://www.hindawi.com/journals/tswj/2014/219580/
It is very time consuming to solve fractional differential equations. The computational complexity of twodimensional fractional differential equation (2DTFDE) with iterative implicit finite difference method is . In this paper, we present a parallel algorithm for 2DTFDE and give an indepth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16–4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future.
Chunye Gong, Weimin Bao, Guojian Tang, Yuewen Jiang, and Jie Liu
Copyright © 2014 Chunye Gong et al. All rights reserved.

An Osgood Type Regularity Criterion for the 3D Boussinesq Equations
Tue, 11 Mar 2014 09:26:20 +0000
http://www.hindawi.com/journals/tswj/2014/563084/
We consider the threedimensional Boussinesq equations, and obtain an Osgood type regularity criterion in terms of the velocity gradient.
Qiang Wu, Lin Hu, and Guili Liu
Copyright © 2014 Qiang Wu et al. All rights reserved.

Minimal Solution of Singular LR Fuzzy Linear Systems
Tue, 11 Mar 2014 00:00:00 +0000
http://www.hindawi.com/journals/tswj/2014/517218/
In this paper, the singular LR fuzzy linear system is introduced. Such systems are divided into two parts: singular consistent LR fuzzy linear systems and singular inconsistent LR fuzzy linear systems. The capability of the generalized inverses such as Drazin inverse, pseudoinverse, and {1}inverse in finding minimal solution of singular consistent LR fuzzy linear systems is investigated.
M. Nikuie and M. Z. Ahmad
Copyright © 2014 M. Nikuie and M. Z. Ahmad. All rights reserved.

Contractive Maps in Locally Transitive Relational Metric Spaces
Mon, 10 Mar 2014 13:49:53 +0000
http://www.hindawi.com/journals/tswj/2014/169358/
Some fixed point results are given for a class of MeirKeeler contractive maps acting on metric spaces endowed with locally transitive relations. Technical connections with the related statements due to Berzig et al. (2014) are also being discussed.
Mihai Turinici
Copyright © 2014 Mihai Turinici. All rights reserved.

Improved DelayDependent Stability Conditions for MIMO Networked Control Systems with Nonlinear Perturbations
Mon, 10 Mar 2014 13:06:10 +0000
http://www.hindawi.com/journals/tswj/2014/196927/
This paper provides improved time delaydependent stability criteria for multiinput and multioutput (MIMO) network control systems (NCSs) with nonlinear perturbations. Without the stability assumption on the neutral operator after the descriptor approach, the new proposed stability theory is less conservative than the existing stability condition. Theoretical proof is given in this paper to demonstrate the effectiveness of the proposed stability condition.
Jiuwen Cao
Copyright © 2014 Jiuwen Cao. All rights reserved.

On the Higher Power Sums of Reciprocal HigherOrder Sequences
Mon, 10 Mar 2014 09:57:08 +0000
http://www.hindawi.com/journals/tswj/2014/521358/
Let be a higherorder linear recursive sequence. In this paper, we use the properties of error estimation and the analytic method to study the reciprocal sums of higher power of higherorder sequences. Then we establish several new and interesting identities relating to the infinite and finite sums.
Zhengang Wu and Jin Zhang
Copyright © 2014 Zhengang Wu and Jin Zhang. All rights reserved.

A Procedure to Construct Exact Solutions of Nonlinear Fractional Differential Equations
Mon, 10 Mar 2014 08:31:38 +0000
http://www.hindawi.com/journals/tswj/2014/489495/
We use the fractional transformation to convert the nonlinear
partial fractional differential equations with the nonlinear ordinary
differential equations. The Expfunction method is extended to solve
fractional partial differential equations in the sense of the modified
RiemannLiouville derivative. We apply the Expfunction method to the
time fractional SharmaTassoOlver equation, the space fractional Burgers
equation, and the time fractional fmKdV equation. As a result, we obtain some
new exact solutions.
Özkan Güner and Adem C. Cevikel
Copyright © 2014 Özkan Güner and Adem C. Cevikel. All rights reserved.

A New Mixed Element Method for a Class of TimeFractional Partial Differential Equations
Sun, 09 Mar 2014 11:16:03 +0000
http://www.hindawi.com/journals/tswj/2014/141467/
A kind of new mixed element method for timefractional partial differential
equations is studied. The Caputofractional derivative of time direction is approximated
by twostep difference method and the spatial direction is discretized by a new mixed element
method, whose gradient belongs to the simple space replacing the complex
space. Some a priori error estimates in norm for the scalar unknown and in norm for its gradient . Moreover, we also discuss a priori error estimates in norm for the scalar unknown .
Yang Liu, Hong Li, Wei Gao, Siriguleng He, and Zhichao Fang
Copyright © 2014 Yang Liu et al. All rights reserved.

An Inequality of Meromorphic Functions and Its Application
Thu, 06 Mar 2014 08:07:33 +0000
http://www.hindawi.com/journals/tswj/2014/242851/
By applying Ahlfors theory of covering surface, we establish a fundamental inequality of meromorphic function dealing with multiple values in an angular domain. As an application, we prove the existence of some new singular directions for a meromorphic function , namely a Bloch direction and a pseudoT direction for .
Zhaojun Wu, Yuxian Chen, and Zuxing Xuan
Copyright © 2014 Zhaojun Wu et al. All rights reserved.

Homotopic Approximate Solutions for the Perturbed CKdV Equation with Variable Coefficients
Wed, 05 Mar 2014 16:41:24 +0000
http://www.hindawi.com/journals/tswj/2014/593642/
This work concerns how to find the double periodic form of approximate solutions of the perturbed combined KdV (CKdV) equation with variable coefficients by using the homotopic mapping method. The obtained solutions may degenerate into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in the limit cases. Moreover, the first order approximate solutions and the second order approximate solutions of the variable coefficients CKdV equation in perturbation are also induced.
Dianchen Lu, Tingting Chen, and Baojian Hong
Copyright © 2014 Dianchen Lu et al. All rights reserved.

On a New Efficient SteffensenLike Iterative Class by Applying a Suitable SelfAccelerator Parameter
Mon, 03 Mar 2014 08:39:12 +0000
http://www.hindawi.com/journals/tswj/2014/769758/
It is attempted to present an efficient and free derivative class of Steffensenlike methods for solving nonlinear equations. To this end, firstly, we construct an optimal eighthorder threestep uniparameter without memory of iterative methods. Then the selfaccelerator parameter is estimated using Newton’s
interpolation in such a way that it improves its convergence order from 8 to 12 without any extra function evaluation. Therefore, its efficiency index is increased from 81/4 to 121/4 which is the main feature of this class. To show applicability of the proposed methods, some numerical illustrations are presented.
Taher Lotfi and Elahe Tavakoli
Copyright © 2014 Taher Lotfi and Elahe Tavakoli. All rights reserved.

Stability of Nonlinear Dirichlet BVPs Governed by Fractional Laplacian
Sun, 02 Mar 2014 14:22:57 +0000
http://www.hindawi.com/journals/tswj/2014/920537/
We consider a class of partial differential equations with the fractional Laplacian and the homogeneous
Dirichlet boundary data. Some sufficient condition under which the solutions of the equations considered depend continuously on parameters is stated. The application of the results to some optimal control problem is presented. The methods applied in the paper make use of the variational structure of the problem.
Dorota Bors
Copyright © 2014 Dorota Bors. All rights reserved.

VIMBased Dynamic Sparse Grid Approach to Partial Differential Equations
Thu, 27 Feb 2014 16:28:30 +0000
http://www.hindawi.com/journals/tswj/2014/390148/
Combining the variational iteration method (VIM) with the sparse grid theory, a dynamic sparse grid approach for nonlinear PDEs is proposed in this paper. In this method, a multilevel interpolation operator is constructed based on the sparse grids theory firstly. The operator is based on the linear combination of the basic functions and independent of them. Second, by means of the precise integration method (PIM), the VIM is developed to solve the nonlinear system of ODEs which is obtained from the discretization of the PDEs. In addition, a dynamic choice scheme on both of the inner and external grid points is proposed. It is different from the traditional interval wavelet collocation method in which the choice of both of the inner and external grid points is dynamic. The numerical experiments show that our method is better than the traditional wavelet collocation method, especially in solving the PDEs with the Nuemann boundary conditions.
ShuLi Mei
Copyright © 2014 ShuLi Mei. All rights reserved.

Stability Analysis of Impulsive Control Systems with Finite and Infinite Delays
Thu, 27 Feb 2014 13:53:19 +0000
http://www.hindawi.com/journals/tswj/2014/932395/
This paper studies impulsive control systems with finite and
infinite delays. Several stability criteria are established by employing
the largest and smallest eigenvalue of matrix. Our sufficient conditions
are less restrictive than the ones in the earlier literature. Moreover,
it is shown that by using impulsive control, the delay systems can be
stabilized even if it contains no stable matrix. Finally, some numerical
examples are discussed to illustrate the theoretical results.
Xuling Wang, Xiaodi Li, and Gani Tr. Stamov
Copyright © 2014 Xuling Wang et al. All rights reserved.

On Positive Radial Solutions for a Class of Elliptic Equations
Tue, 25 Feb 2014 07:18:10 +0000
http://www.hindawi.com/journals/tswj/2014/507312/
A class of elliptic boundary value problem in an exterior domain is considered under some conditions concerning the first eigenvalue of the relevant linear operator, where the variables of nonlinear term need not to be separated. Several new theorems on the existence and multiplicity of positive radial solutions are obtained by means of fixed point index theory. Our conclusions are essential improvements of the results in Lan and Webb (1998), Lee (1997), Mao and Xue (2002), Stańczy (2000), and Han and Wang (2006).
Ying Wu and Guodong Han
Copyright © 2014 Ying Wu and Guodong Han. All rights reserved.

Nonprobabilistic Solution of Uncertain Vibration Equation of Large Membranes Using Adomian Decomposition Method
Mon, 24 Feb 2014 09:32:29 +0000
http://www.hindawi.com/journals/tswj/2014/308205/
This paper proposes a new technique based on double parametric form of fuzzy numbers to handle the uncertain vibration equation for very large membrane for different particular cases. Uncertainties present in the initial condition and the wave velocity of free vibration are modelled through Gaussian convex normalised fuzzy set. Using the single parametric form of fuzzy number, the original fuzzy vibration equation is converted first to an interval fuzzy vibration equation. Next this equation is transformed to crisp form by applying double parametric form of fuzzy numbers. Finally the same governing equation is solved by Adomian decomposition method (ADM) symbolically to obtain the uncertain bounds. The present methods are very simple and effective. Obtained results are depicted in terms of plots to show the efficiency and powerfulness of the present analysis. Results obtained by the methods with new techniques are compared with existing results in special cases.
Smita Tapaswini and S. Chakraverty
Copyright © 2014 Smita Tapaswini and S. Chakraverty. All rights reserved.

Multiple Control Strategies for Prevention of Avian Influenza Pandemic
Mon, 24 Feb 2014 08:12:47 +0000
http://www.hindawi.com/journals/tswj/2014/949718/
We present the prevention of avian influenza pandemic by adjusting multiple control functions in the humantohuman transmittable avian influenza model. First we show the existence of the optimal control problem; then by using both analytical and
numerical techniques, we investigate the costeffective control effects for the prevention of transmission of disease. To do this, we use three control functions, the effort to reduce the number of contacts with human infected with mutant avian influenza, the antiviral treatment of infected individuals, and the effort to reduce the number of infected birds. We completely characterized the optimal control and compute numerical solution of the optimality system by using an iterative method.
Roman Ullah, Gul Zaman, and Saeed Islam
Copyright © 2014 Roman Ullah et al. All rights reserved.

Analysis of EyringPowell Fluid in Helical Screw Rheometer
Mon, 24 Feb 2014 08:07:51 +0000
http://www.hindawi.com/journals/tswj/2014/143968/
This paper aims to study the flow of an incompressible, isothermal EyringPowell fluid in a helical screw rheometer. The complicated geometry of the helical screw rheometer is simplified by “unwrapping or flattening” the channel, lands, and the outside rotating barrel, assuming the width of the channel is larger as compared to the depth. The developed second order nonlinear differential equations are solved by using Adomian decomposition method. Analytical expressions are obtained for the velocity profiles, shear stresses, shear at wall, force exerted on fluid, volume flow rates, and average velocity. The effect of nonNewtonian parameters, pressure gradients, and flight angle on the velocity profiles is noticed with the help of graphical representation. The observation confirmed the vital role of involved parameters during the extrusion process.
A. M. Siddiqui, T. Haroon, and M. Zeb
Copyright © 2014 A. M. Siddiqui et al. All rights reserved.

A GaussKuzmin Theorem for Continued Fractions Associated with Nonpositive Integer Powers of an Integer
Sun, 23 Feb 2014 13:57:39 +0000
http://www.hindawi.com/journals/tswj/2014/984650/
We consider a family of interval maps which are generalizations of the Gauss transformation.
For the continued fraction expansion arising from , we solve a GaussKuzmintype problem.
Dan Lascu
Copyright © 2014 Dan Lascu. All rights reserved.

Control Problems for Semilinear Neutral Differential Equations in Hilbert Spaces
Sun, 23 Feb 2014 00:00:00 +0000
http://www.hindawi.com/journals/tswj/2014/431978/
We construct some results on the regularity of solutions and the approximate controllability for neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the controllability of the neutral equations, we first consider the existence and regularity of solutions of the neutral control system by using fractional power of operators and the local Lipschitz continuity of nonlinear term. Our purpose is to obtain the existence of solutions and the approximate controllability for neutral functional differential control systems without using many of the strong restrictions considered in the previous literature. Finally we give a simple example to which our main result can be applied.
JinMun Jeong and Seong Ho Cho
Copyright © 2014 JinMun Jeong and Seong Ho Cho. All rights reserved.

Some New Type Sigma Convergent Sequence Spaces and Some New Inequalities
Thu, 20 Feb 2014 13:38:49 +0000
http://www.hindawi.com/journals/tswj/2014/589765/
We have discussed some important problems about the spaces and of Cesàro sigma convergent and Cesàro null sequence.
Kuddusi Kayaduman and Mehmet Şengönül
Copyright © 2014 Kuddusi Kayaduman and Mehmet Şengönül. All rights reserved.

Definition and Properties of the Libera Operator on Mixed Norm Spaces
Thu, 20 Feb 2014 11:14:48 +0000
http://www.hindawi.com/journals/tswj/2014/590656/
We consider the action of the operator on a class of “mixed norm” spaces of analytic functions on the unit disk, , defined by the requirement , where , , , and is a nonnegative integer. This class contains Besov spaces, weighted Bergman spaces, Dirichlet type spaces, HardySobolev spaces, and so forth. The expression need not be defined for analytic in the unit disk, even for . A sufficient, but not necessary, condition is that . We identify the indices , , , and for which is well defined on , acts from to , the implication holds. Assertion extends some known results, due to Siskakis and others, and contains some new ones. As an application of we have a generalization of Bernstein’s theorem on absolute convergence of power series that belong to a Hölder class.
Miroslav Pavlovic
Copyright © 2014 Miroslav Pavlovic. All rights reserved.

Approximate Series Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology
Thu, 20 Feb 2014 08:54:44 +0000
http://www.hindawi.com/journals/tswj/2014/945872/
We introduce an efficient recursive scheme based on Adomian decomposition
method (ADM) for solving nonlinear singular boundary value problems. This approach is based on a modification of the ADM; here we use all the boundary conditions to derive an integral equation before establishing the recursive scheme for the solution components. In fact, we develop the recursive scheme without any undetermined coefficients while computing the solution components. Unlike the classical ADM, the proposed method avoids solving a sequence of nonlinear algebraic or transcendental equations for the undetermined coefficients. The approximate solution is obtained in the form of series with easily calculable components. The uniqueness of the solution is discussed. The convergence and error
analysis of the proposed method are also established. The accuracy and reliability of the proposed method are examined by four numerical examples.
Randhir Singh, Jitendra Kumar, and Gnaneshwar Nelakanti
Copyright © 2014 Randhir Singh et al. All rights reserved.

Strong Convergence Algorithm for Split Equilibrium Problems and Hierarchical Fixed Point Problems
Thu, 20 Feb 2014 00:00:00 +0000
http://www.hindawi.com/journals/tswj/2014/390956/
The purpose of this paper is to investigate the problem of finding the approximate element of the common set of solutions of a split equilibrium problem and a hierarchical fixed point problem in a real Hilbert space. We establish the strong convergence of the proposed method under some mild conditions. Several special cases are also discussed. Our main result extends and improves some wellknown results in the literature.
Abdellah Bnouhachem
Copyright © 2014 Abdellah Bnouhachem. All rights reserved.

New Stabilization for Dynamical System with Two Additive TimeVarying Delays
Tue, 18 Feb 2014 14:51:18 +0000
http://www.hindawi.com/journals/tswj/2014/315817/
This paper provides a new delaydependent stabilization criterion for systems with two additive timevarying delays. The novel functional is constructed, a tighter upper bound
of the derivative of the Lyapunov functional is obtained. These results have advantages over some existing ones because the combination of the delay decomposition technique and the reciprocally convex approach. Two examples are provided to demonstrate the less conservatism and effectiveness of the results in this paper.
Lianglin Xiong, Fan Yang, and Xiaozhou Chen
Copyright © 2014 Lianglin Xiong et al. All rights reserved.

A New Expanded Mixed Element Method for ConvectionDominated Sobolev Equation
Tue, 18 Feb 2014 13:07:49 +0000
http://www.hindawi.com/journals/tswj/2014/297825/
We propose and analyze a new expanded mixed element method, whose gradient belongs to the simple square integrable space instead of the classical H(div; Ω) space of Chen’s expanded mixed element method. We study the new expanded mixed element method for convectiondominated Sobolev equation, prove the existence and uniqueness for finite element solution, and introduce a new expanded mixed projection. We derive the optimal a priori error estimates in norm for the scalar unknown and a priori error estimates in norm for its gradient λ and its flux σ. Moreover, we obtain the optimal a priori error estimates in norm for the scalar unknown u. Finally, we obtained some numerical results to illustrate efficiency of the new method.
Jinfeng Wang, Yang Liu, Hong Li, and Zhichao Fang
Copyright © 2014 Jinfeng Wang et al. All rights reserved.

Local Generalized ()Derivations
Sun, 16 Feb 2014 15:25:18 +0000
http://www.hindawi.com/journals/tswj/2014/805780/
We study local generalized ()derivations on algebras generated by their idempotents and give some important applications of our results.
Ajda Fošner
Copyright © 2014 Ajda Fošner. All rights reserved.

A Class of Nonlocal Coupled Semilinear Parabolic System with Nonlocal Boundaries
Sun, 16 Feb 2014 13:21:03 +0000
http://www.hindawi.com/journals/tswj/2014/912356/
We investigate the positive solutions of the semilinear parabolic
system with coupled nonlinear nonlocal sources subject to weighted nonlocal Dirichlet boundary
conditions. The blowup and global existence criteria are obtained.
Hong Liu and Haihua Lu
Copyright © 2014 Hong Liu and Haihua Lu. All rights reserved.

HighOrder Compact Difference Scheme for the Numerical Solution of Time Fractional Heat Equations
Thu, 13 Feb 2014 16:07:21 +0000
http://www.hindawi.com/journals/tswj/2014/642989/
A highorder finite difference scheme is proposed for solving time fractional heat equations. The time fractional derivative is described in the RiemannLiouville sense. In the proposed scheme a new secondorder discretization, which is based on CrankNicholson method, is applied for the time fractional part and fourthorder accuracy compact approximation is applied for the secondorder space derivative. The spectral stability and the Fourier stability analysis of the difference scheme are shown. Finally a detailed numerical analysis, including tables, figures, and error comparison, is given to demonstrate the theoretical results and high accuracy of the proposed scheme.
Ibrahim Karatay and Serife R. Bayramoglu
Copyright © 2014 Ibrahim Karatay and Serife R. Bayramoglu. All rights reserved.

About Positivity of Green's Functions for Nonlocal Boundary Value Problems with Impulsive Delay Equations
Thu, 13 Feb 2014 09:22:53 +0000
http://www.hindawi.com/journals/tswj/2014/978519/
The impulsive delay differential equation is considered with nonlocal boundary condition Various results on existence and uniqueness of solutions and on positivity/negativity of the Green's functions for this equation are obtained.
Alexander Domoshnitsky and Irina Volinsky
Copyright © 2014 Alexander Domoshnitsky and Irina Volinsky. All rights reserved.

Stability, Boundedness, and Lagrange Stability of Fractional Differential Equations with Initial Time Difference
Wed, 12 Feb 2014 06:55:23 +0000
http://www.hindawi.com/journals/tswj/2014/939027/
Differential inequalities, comparison results, and sufficient conditions on initial time difference stability, boundedness, and Lagrange stability for fractional differential systems have been evaluated.
Muhammed Çiçek, Coşkun Yakar, and Bülent Oğur
Copyright © 2014 Muhammed Çiçek et al. All rights reserved.

Some New Traveling Wave Exact Solutions of the (2+1)Dimensional BoitiLeonPempinelli Equations
Tue, 11 Feb 2014 11:44:48 +0000
http://www.hindawi.com/journals/tswj/2014/743254/
We employ the complex method to obtain all meromorphic exact solutions of complex (2+1)dimensional BoitiLeonPempinelli equations (BLP system of equations). The idea introduced in this paper can be applied to other nonlinear evolution equations.
Our results show that all rational and simply periodic traveling wave exact solutions of the equations (BLP) are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions and simply periodic solutions which are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role for finding exact solutions in the mathematical physics. For these new traveling wave solutions, we give some computer simulations to illustrate our main results.
Jianming Qi, Fu Zhang, Wenjun Yuan, and Zifeng Huang
Copyright © 2014 Jianming Qi et al. All rights reserved.

Fixed Point Results for Generalized Chatterjea Type Contractive Conditions in Partially Ordered Metric Spaces
Tue, 11 Feb 2014 09:16:01 +0000
http://www.hindawi.com/journals/tswj/2014/341751/
In the framework of ordered metric spaces, fixed points of maps that satisfy the generalized Chatterjea type contractive conditions are obtained. The results presented in the paper generalize and extend several well known comparable results in the literature.
Safeer Hussain Khan, Mujahid Abbas, and Talat Nazir
Copyright © 2014 Safeer Hussain Khan et al. All rights reserved.

A Study of Frontier and Semifrontier in Intuitionistic Fuzzy Topological Spaces
Tue, 11 Feb 2014 06:39:22 +0000
http://www.hindawi.com/journals/tswj/2014/674171/
Notions of frontier and semifrontier in intuitionistic fuzzy topology have been studied and several of their properties, characterizations, and examples established. Many counterexamples have been presented to point divergences between the IF topology and its classical form. The paper also presents an open problem and one of its weaker forms.
Athar Kharal
Copyright © 2014 Athar Kharal. All rights reserved.

Approximation of Bivariate Functions via Smooth Extensions
Mon, 10 Feb 2014 13:53:22 +0000
http://www.hindawi.com/journals/tswj/2014/102062/
For a smooth bivariate function defined on a general domain with arbitrary shape, it is
difficult to do Fourier approximation or wavelet approximation. In order to solve these problems, in this paper,
we give an extension of the bivariate function on a general domain with arbitrary shape to a smooth, periodic
function in the whole space or to a smooth, compactly supported function in the whole space. These smooth
extensions have simple and clear representations which are determined by this bivariate function and some
polynomials. After that, we expand the smooth, periodic function into a Fourier series or a periodic wavelet
series or we expand the smooth, compactly supported function into a wavelet series. Since our extensions are
smooth, the obtained Fourier coefficients or wavelet coefficients decay very fast. Since our extension tools are
polynomials, the moment theorem shows that a lot of wavelet coefficients vanish. From this, with the help of
wellknown approximation theorems, using our extension methods, the Fourier approximation and the wavelet
approximation of the bivariate function on the general domain with small error are obtained.
Zhihua Zhang
Copyright © 2014 Zhihua Zhang. All rights reserved.

Some Properties of Solutions of a FunctionalDifferential Equation of Second Order with Delay
Mon, 10 Feb 2014 13:05:29 +0000
http://www.hindawi.com/journals/tswj/2014/878395/
Existence, uniqueness, data dependence (monotony, continuity, and differentiability with respect to parameter), and UlamHyers stability results for the solutions of a system of functionaldifferential equations with delays are proved. The techniques used are Perov’s fixed point theorem and weakly Picard operator theory.
Veronica Ana Ilea and Diana Otrocol
Copyright © 2014 Veronica Ana Ilea and Diana Otrocol. All rights reserved.

Generalized Uniqueness Theorem for Ordinary Differential Equations in Banach Spaces
Mon, 10 Feb 2014 09:05:32 +0000
http://www.hindawi.com/journals/tswj/2014/272479/
We consider nonlinear ordinary differential equations in Banach spaces. Uniqueness criterion for the Cauchy problem is given when any of the standard dissipativetype conditions does apply. A similar scalar result has been studied by Majorana (1991). Useful examples of reflexive Banach spaces whose positive cones have empty interior has been given as well.
Ezzat R. Hassan, M. Sh. Alhuthali, and M. M. AlGhanmi
Copyright © 2014 Ezzat R. Hassan et al. All rights reserved.

On Statistical Convergence of Order
Sun, 09 Feb 2014 09:48:44 +0000
http://www.hindawi.com/journals/tswj/2014/535419/
The idea of convergence of real sequences was introduced by Kostyrko et al., (2000/01) and also independently by Nuray and Ruckle (2000). In this paper, we introduce the concepts of statistical convergence of order and strong Cesàro summability of order of real sequences and investigated their relationship.
Mikail Et, Abdullah Alotaibi, and S. A. Mohiuddine
Copyright © 2014 Mikail Et et al. All rights reserved.

On the Singular Perturbations for Fractional Differential Equation
Sun, 09 Feb 2014 07:47:10 +0000
http://www.hindawi.com/journals/tswj/2014/752371/
The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.
Abdon Atangana
Copyright © 2014 Abdon Atangana. All rights reserved.

A New HighOrder Stable Numerical Method for Matrix Inversion
Thu, 06 Feb 2014 17:06:47 +0000
http://www.hindawi.com/journals/tswj/2014/830564/
A stable numerical method is proposed for matrix inversion. The new method is accompanied by theoretical proof to illustrate twelfthorder convergence. A discussion of how to achieve the convergence using an appropriate initial value is presented. The application of the new scheme for finding MoorePenrose inverse will also be pointed out analytically. The efficiency of the contributed iterative method is clarified on solving some numerical examples.
F. Khaksar Haghani and F. Soleymani
Copyright © 2014 F. Khaksar Haghani and F. Soleymani. All rights reserved.

Fuzzy Fixed Points Theorems for Fuzzy Mappings via Admissible Pair
Wed, 05 Feb 2014 11:43:34 +0000
http://www.hindawi.com/journals/tswj/2014/853032/
We define the concept of admissible for a pair of fuzzy mappings and establish the existence of common fuzzy fixed point theorem. Our result generalizes some useful results in the literature. We provide an example to support our result.
Maliha Rashid, Akbar Azam, and Nayyar Mehmood
Copyright © 2014 Maliha Rashid et al. All rights reserved.

Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations
Tue, 04 Feb 2014 11:20:53 +0000
http://www.hindawi.com/journals/tswj/2014/497393/
Finite difference technique is applied to numerical solution of the initialboundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities twolevel difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown.
I. Amirali, G. M. Amiraliyev, M. Cakir, and E. Cimen
Copyright © 2014 I. Amirali et al. All rights reserved.

Coefficient Inequalities for a Subclass of pValent Analytic Functions
Tue, 04 Feb 2014 00:00:00 +0000
http://www.hindawi.com/journals/tswj/2014/801751/
The aim of this paper is to study the problem of coefficient bounds for a newly defined subclass of pvalent analytic functions. Many known results appear as special consequences of our work.
Muhammad Arif, Janusz Sokół, and Muhammad Ayaz
Copyright © 2014 Muhammad Arif et al. All rights reserved.

On the Long Time Simulation of ReactionDiffusion Equations with Delay
Mon, 03 Feb 2014 06:42:28 +0000
http://www.hindawi.com/journals/tswj/2014/186802/
For a consistent numerical method to be practically useful, it is widely accepted that it must preserve the asymptotic stability of the original continuous problem. However, in this study, we show that it may lead to unreliable numerical solutions in long time simulation even if a classical numerical method gives a larger stability region than that of the original continuous problem. Some numerical experiments on the reactiondiffusion equations with delay are presented to confirm our findings. Finally, some open problems on the subject are proposed.
Dongfang Li and Chengjian Zhang
Copyright © 2014 Dongfang Li and Chengjian Zhang. All rights reserved.

Dynamics of a Diffusive PredatorPrey Model with General Nonlinear Functional Response
Mon, 03 Feb 2014 06:29:19 +0000
http://www.hindawi.com/journals/tswj/2014/721403/
We study a diffusive predatorprey model with nonconstant death rate and general nonlinear functional response. Firstly, stability analysis of the equilibrium for reduced ODE system is discussed. Secondly, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. Furthermore, sufficient conditions for the global asymptotical stability of the unique positive equilibrium of the system are derived by using the method of Lyapunov function. Finally, we show that there are no nontrivial steady state solutions for certain parameter configuration.
Wensheng Yang
Copyright © 2014 Wensheng Yang. All rights reserved.

PPF Dependent Fixed Point Results for Triangular Admissible Mappings
Sun, 02 Feb 2014 08:35:09 +0000
http://www.hindawi.com/journals/tswj/2014/673647/
We introduce the concept of triangular admissible
mappings (pair of mappings) with respect to nonselfmappings and
establish the existence of PPF dependent fixed (coincidence) point theorems
for contraction mappings involving triangular admissible mappings
(pair of mappings) with respect to nonselfmappings in Razumikhin
class. Several interesting consequences of our theorems are also given.
Ljubomir Ćirić, Saud M. Alsulami, Peyman Salimi, and Pasquale Vetro
Copyright © 2014 Ljubomir Ćirić et al. All rights reserved.

Nature Inspired Computational Technique for the Numerical Solution of Nonlinear Singular Boundary Value Problems Arising in Physiology
Sun, 02 Feb 2014 07:20:04 +0000
http://www.hindawi.com/journals/tswj/2014/837021/
We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE) and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA), interior point algorithm (IPA), and active set algorithm (ASA). The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.
Suheel Abdullah Malik, Ijaz Mansoor Qureshi, Muhammad Amir, and Ihsanul Haq
Copyright © 2014 Suheel Abdullah Malik et al. All rights reserved.

The NonRelativistic Limit for the eMHD Equations
Thu, 30 Jan 2014 09:36:27 +0000
http://www.hindawi.com/journals/tswj/2014/261082/
We investigate the nonrelativistic limit for the eMHD equations in a threedimension unit periodic torus. With the prepared initial data, our result shows that the small parameter problems have unique solutions existing in the finite time interval where the corresponding limit problems (incompressible Euler equations) have smooth solutions. Moreover, the formal limit is rigorously justified.
Hongli Wang and Jie Zhao
Copyright © 2014 Hongli Wang and Jie Zhao. All rights reserved.

Milloux Inequality of EValued Meromorphic Function
Thu, 30 Jan 2014 08:29:18 +0000
http://www.hindawi.com/journals/tswj/2014/861573/
The main purpose of this paper is to establish the Milloux inequality of valued meromorphic function from the complex plane to an infinite dimensional complex Banach space with a Schauder basis. As an application, we study the Borel exceptional values of an valued meromorphic function and those of its derivatives; results are obtained to extend some related results for meromorphic scalarvalued function of Singh, Gopalakrishna, and Bhoosnurmath.
Zhaojun Wu and Zuxing Xuan
Copyright © 2014 Zhaojun Wu and Zuxing Xuan. All rights reserved.

Expansion Method and New Exact Solutions of
the SchrödingerKdV Equation
Wed, 29 Jan 2014 13:09:12 +0000
http://www.hindawi.com/journals/tswj/2014/534063/
expansion method is proposed to seek exact solutions of nonlinear evolution equations. With the aid of symbolic computation, we choose the SchrödingerKdV equation with a source to illustrate the validity and advantages of the proposed method. A number of Jacobielliptic function solutions are obtained including the Weierstrasselliptic function solutions. When the modulus m of Jacobielliptic function approaches to 1 and 0, solitonlike solutions and trigonometricfunction solutions are also obtained, respectively. The proposed method is a straightforward, short, promising, and powerful method for the nonlinear evolution equations in mathematical physics.
Ali Filiz, Mehmet Ekici, and Abdullah Sonmezoglu
Copyright © 2014 Ali Filiz et al. All rights reserved.

Partial Rectangular Metric Spaces and Fixed Point Theorems
Wed, 29 Jan 2014 09:59:44 +0000
http://www.hindawi.com/journals/tswj/2014/756298/
The purpose of this paper is to introduce the concept of partial rectangular metric spaces as a generalization of rectangular metric and partial metric spaces. Some properties of partial rectangular metric spaces and some fixed point results for quasitype contraction in partial rectangular metric spaces are proved. Some examples are given to illustrate the observed results.
Satish Shukla
Copyright © 2014 Satish Shukla. All rights reserved.

HighAccuracy Approximation of HighRank Derivatives: Isotropic Finite Differences Based on LatticeBoltzmann Stencils
Wed, 29 Jan 2014 06:55:21 +0000
http://www.hindawi.com/journals/tswj/2014/142907/
We propose isotropic finite differences for highaccuracy approximation of highrank derivatives. These finite differences are based on direct application of latticeBoltzmann stencils. The presented finitedifference expressions are valid in any dimension, particularly in two and three dimensions, and any latticeBoltzmann stencil isotropic enough can be utilized. A theoretical basis for the proposed utilization of latticeBoltzmann stencils in the approximation of highrank derivatives is established. In particular, the isotropy and accuracy properties of the proposed approximations are derived directly from this basis. Furthermore, in this formal development, we extend the theory of Hermite polynomial tensors in the case of discrete spaces and present expressions for the discrete inner products between monomials and Hermite polynomial tensors. In addition, we prove an equivalency between two approaches for constructing latticeBoltzmann stencils. For the numerical verification of the presented finite differences, we introduce 5th, 6th, and 8thorder twodimensional latticeBoltzmann stencils.
Keijo Kalervo Mattila, Luiz Adolfo Hegele Júnior, and Paulo Cesar Philippi
Copyright © 2014 Keijo Kalervo Mattila et al. All rights reserved.

Sumudu Transforms of Analogues of Bessel Functions
Wed, 29 Jan 2014 00:00:00 +0000
http://www.hindawi.com/journals/tswj/2014/327019/
The main purpose of this paper is to evaluate Sumudu transforms of a product
of Bessel functions. Interesting special cases of theorems are also
discussed. Further, the results proved in this paper may find certain
applications of Sumudu transforms to the solutions of the integrodifferential equations involving Bessel functions. The results
may help to extend the theory of orthogonal functions.
Faruk Uçar
Copyright © 2014 Faruk Uçar. All rights reserved.

On Algebras of Holomorphic Functions
Tue, 28 Jan 2014 10:53:35 +0000
http://www.hindawi.com/journals/tswj/2014/901726/
We consider the classes of holomorphic functions on the open unit disk in the complex plane. These classes are in fact generalizations of the class introduced by Kim (1986). The space equipped with the topology given by the metric defined by , with and , becomes an space. By a result of Stoll (1977), the Privalov space with the topology given by the Stoll metric is an algebra. By using these two facts, we prove that the spaces and coincide and have the same topological structure. Consequently, we describe a general form of continuous linear functionals on (with respect to the metric ). Furthermore, we give a characterization of bounded subsets of the spaces . Moreover, we give the examples of bounded subsets of that are not relatively compact.
Romeo Meštrović
Copyright © 2014 Romeo Meštrović. All rights reserved.

Spaces of Ideal Convergent Sequences
Tue, 28 Jan 2014 09:25:12 +0000
http://www.hindawi.com/journals/tswj/2014/134534/
In the present paper, we introduce some sequence spaces using ideal convergence and MusielakOrlicz function . We also examine some topological properties of the resulting sequence spaces.
M. Mursaleen and Sunil K. Sharma
Copyright © 2014 M. Mursaleen and Sunil K. Sharma. All rights reserved.

Existence of Limit Cycles in the Solow Model with DelayedLogistic Population Growth
Tue, 28 Jan 2014 09:15:41 +0000
http://www.hindawi.com/journals/tswj/2014/207806/
This paper is devoted to the existence and stability analysis of limit cycles in a delayed
mathematical model for the economy growth. Specifically the Solow model is further
improved by inserting the time delay into the logistic population growth rate. Moreover,
by choosing the time delay as a bifurcation parameter, we prove that the system loses its
stability and a Hopf bifurcation occurs when time delay passes through critical values.
Finally, numerical simulations are carried out for supporting the analytical results.
Carlo Bianca and Luca Guerrini
Copyright © 2014 Carlo Bianca and Luca Guerrini. All rights reserved.

Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities
Tue, 28 Jan 2014 07:25:00 +0000
http://www.hindawi.com/journals/tswj/2014/278305/
The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel timedomain and frequencydomain criteria are established by using the Lyapunov method and the wellknown KalmanYakubovichPopov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.
Xian Liu, Jiajia Du, and Qing Gao
Copyright © 2014 Xian Liu et al. All rights reserved.

An Analytical Study for (2 + 1)Dimensional Schrödinger Equation
Mon, 27 Jan 2014 08:30:17 +0000
http://www.hindawi.com/journals/tswj/2014/438345/
In this paper, the homotopy analysis method has been applied to solve (2 + 1)dimensional Schrödinger equations. The validity of this method has successfully been accomplished by applying it to find the solution of some of its variety forms. The results obtained by homotopy analysis method have been compared with those of exact solutions. The main objective is to propose alternative methods of finding a solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. The results show that the solution of homotopy analysis method is in a good agreement with the exact solution.
Behzad Ghanbari
Copyright © 2014 Behzad Ghanbari. All rights reserved.

Two LegendreDualPetrovGalerkin Algorithms for Solving the Integrated Forms of High OddOrder Boundary Value Problems
Mon, 27 Jan 2014 07:59:19 +0000
http://www.hindawi.com/journals/tswj/2014/309264/
Two numerical algorithms based on dualPetrovGalerkin method are developed for solving the integrated forms of high oddorder boundary value problems (BVPs) governed by homogeneous and nonhomogeneous boundary conditions. Two different choices of trial functions and test functions which satisfy the underlying boundary conditions of the differential equations and the dual boundary conditions are used for this purpose. These choices lead to linear systems with specially structured matrices that can be efficiently inverted, hence greatly reducing the cost. The various matrix systems resulting from these discretizations are carefully investigated, especially their complexities and their condition numbers. Numerical results are given to illustrate the efficiency of the proposed algorithms, and some comparisons with some other methods are made.
Waleed M. AbdElhameed, Eid H. Doha, and Mahmoud A. Bassuony
Copyright © 2014 Waleed M. AbdElhameed et al. All rights reserved.

Stability of a Quartic Functional Equation
Thu, 23 Jan 2014 16:26:11 +0000
http://www.hindawi.com/journals/tswj/2014/752146/
We obtain the general solution of the generalized quartic functional equation + for a fixed positive integer . We prove the HyersUlam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the HyersUlam stability for the mentioned quartic functional equation in nonArchimedean spaces.
Abasalt Bodaghi
Copyright © 2014 Abasalt Bodaghi. All rights reserved.

A New Sixth Order Method for Nonlinear Equations in R
Thu, 23 Jan 2014 12:31:16 +0000
http://www.hindawi.com/journals/tswj/2014/890138/
A new iterative method is described for finding the real roots of nonlinear equations in R. Starting with a suitably chosen , the method generates a sequence of iterates converging to the root. The convergence analysis is provided to establish its sixth order of convergence. The number of iterations and the total number of function evaluations used to get a simple root are taken as performance measure of our method. The efficacy of the method is tested on a number of numerical examples and the results obtained are summarized in tables. It is observed that our method is superior to Newton’s method and other sixth order methods considered.
Sukhjit Singh and D. K. Gupta
Copyright © 2014 Sukhjit Singh and D. K. Gupta. All rights reserved.

A Hybrid Common Fixed Point Theorem under Certain Recent Properties
Thu, 23 Jan 2014 11:16:01 +0000
http://www.hindawi.com/journals/tswj/2014/860436/
We prove a common fixed point theorem for a hybrid pair of
occasionally coincidentally idempotent mappings via common limit range property. Our result
improves some results from the existing literature, especially the ones contained in Sintunavarat
and Kumam (2009). Some illustrative and
interesting examples to highlight the realized improvements are also furnished.
Zoran Kadelburg, Sunny Chauhan, and Mohammad Imdad
Copyright © 2014 Zoran Kadelburg et al. All rights reserved.

Generalized UlamHyers Stability, WellPosedness, and Limit Shadowing of Fixed Point Problems for αβContraction Mapping in Metric Spaces
Thu, 23 Jan 2014 10:58:09 +0000
http://www.hindawi.com/journals/tswj/2014/569174/
We study the generalized UlamHyers stability, the wellposedness, and the limit shadowing of the fixed point problem for new type of generalized contraction mapping, the socalled αβcontraction mapping. Our results in this paper are generalized and unify several results in the literature as the result of Geraghty (1973) and the Banach contraction principle.
Wutiphol Sintunavarat
Copyright © 2014 Wutiphol Sintunavarat. All rights reserved.

Roughness of Nonuniform Exponential Dichotomy for Difference Equations in Banach Spaces
Thu, 23 Jan 2014 09:15:01 +0000
http://www.hindawi.com/journals/tswj/2014/819046/
In this paper we study the roughness of nonuniform exponential dichotomy for nonautonomous difference equations in the general context of infinitedimensional spaces. An explicit form is given for each of the dichotomy constants of the perturbed equation in terms of the original ones. We emphasize that we do not assume any boundedness condition on the coefficients.
Nicolae Lupa
Copyright © 2014 Nicolae Lupa. All rights reserved.

Feedback Control in a General Almost Periodic Discrete System of Plankton Allelopathy
Thu, 23 Jan 2014 06:45:09 +0000
http://www.hindawi.com/journals/tswj/2014/824801/
We study the properties of almost periodic solutions for a general discrete system of plankton allelopathy with feedback controls and establish a theorem on the uniformly asymptotic stability of almost periodic solutions.
Wenshuang Yin
Copyright © 2014 Wenshuang Yin. All rights reserved.

Multiple Positive Solutions to Nonlinear Boundary Value Problems of a System for Fractional Differential Equations
Thu, 23 Jan 2014 06:42:27 +0000
http://www.hindawi.com/journals/tswj/2014/817542/
By using Krasnoselskii's fixed point theorem, we study the existence of at least one or two positive solutions to a system of fractional boundary value problems given by where is the standard RiemannLiouville fractional derivative, for and , subject to the boundary conditions , for , and , for , or , for , and , , for , Our results are new and complement previously known results. As an application, we also give an example to demonstrate our result.
Chengbo Zhai and Mengru Hao
Copyright © 2014 Chengbo Zhai and Mengru Hao. All rights reserved.

Some Inequalities for the Analogue of the Classical Riemann Zeta Functions and the Polygamma Functions
Wed, 22 Jan 2014 10:20:05 +0000
http://www.hindawi.com/journals/tswj/2014/543593/
We present the generalizations on some inequalities for the analogue of the classical Riemann zeta functions and the polygamma functions.
Banyat Sroysang
Copyright © 2014 Banyat Sroysang. All rights reserved.

Approximate Solution of TimeFractional AdvectionDispersion Equation via Fractional Variational Iteration Method
Wed, 22 Jan 2014 10:04:11 +0000
http://www.hindawi.com/journals/tswj/2014/769713/
This paper aims to obtain the approximate solution of timefractional advectiondispersion equation (FADE) involving Jumarie’s modification of RiemannLiouville derivative by the fractional variational iteration method (FVIM). FVIM provides an analytical approximate solution in the form of a convergent series. Some examples are given and the results indicate that the FVIM is of high accuracy, more efficient, and more convenient for solving time FADEs.
Birol İbiş and Mustafa Bayram
Copyright © 2014 Birol İbiş and Mustafa Bayram. All rights reserved.

Multisynchronization of Chaotic Oscillators via Nonlinear Observer Approach
Tue, 21 Jan 2014 13:08:50 +0000
http://www.hindawi.com/journals/tswj/2014/935163/
The goal of this work is to synchronize a class of chaotic oscillators in a masterslave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves’ oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology.
Ricardo AguilarLópez, Rafael MartínezGuerra, and Juan L. MataMachuca
Copyright © 2014 Ricardo AguilarLópez et al. All rights reserved.

A Study of Impulsive Multiterm Fractional Differential Equations with Single and Multiple Base Points and Applications
Tue, 21 Jan 2014 11:22:06 +0000
http://www.hindawi.com/journals/tswj/2014/194346/
We discuss the existence and uniqueness of solutions for initial value problems of nonlinear singular multiterm impulsive Caputo type fractional differential equations on the half line. Our study includes the cases for a single base point fractional differential equation as well as multiple base points fractional differential equation. The asymptotic behavior of solutions for the problems is also investigated. We demonstrate the utility of our work by applying the main results to fractionalorder logistic models.
Yuji Liu and Bashir Ahmad
Copyright © 2014 Yuji Liu and Bashir Ahmad. All rights reserved.

Dynamic Behavior of Positive Solutions for a Leslie PredatorPrey System with Mutual Interference and Feedback Controls
Mon, 20 Jan 2014 13:51:11 +0000
http://www.hindawi.com/journals/tswj/2014/637026/
We consider a Leslie predatorprey system with mutual interference and feedback controls. For general nonautonomous case, by using differential inequality theory and constructing a suitable Lyapunov functional, we obtain some sufficient conditions which guarantee the permanence and the global attractivity of the system. For the periodic case, we obtain some sufficient conditions which guarantee the existence, uniqueness, and stability of a positive periodic solution.
Cong Zhang, Nanjing Huang, and Chuanxian Deng
Copyright © 2014 Cong Zhang et al. All rights reserved.

Controllability and Observability of Fractional Linear Systems with Two Different Orders
Mon, 20 Jan 2014 13:51:02 +0000
http://www.hindawi.com/journals/tswj/2014/618162/
This paper is concerned with the controllability and observability for a class of fractional linear systems with two different orders. The sufficient and necessary conditions for state controllability and state observability of such systems are established. The results obtained extend some existing results of controllability and observability for fractional dynamical systems.
Dengguo Xu, Yanmei Li, and Weifeng Zhou
Copyright © 2014 Dengguo Xu et al. All rights reserved.

Practical Stability in terms of Two Measures for Set Differential Equations on Time Scales
Mon, 20 Jan 2014 10:13:21 +0000
http://www.hindawi.com/journals/tswj/2014/241034/
We present a new comparison principle by introducing a notion of upper quasimonotone nondecreasing and obtain the practical stability criteria for set valued differential equations in terms of two measures on time scales by using the vector Lyapunov function together with the new comparison principle.
Peiguang Wang and Weiwei Sun
Copyright © 2014 Peiguang Wang and Weiwei Sun. All rights reserved.

Approximate Solution of Urysohn Integral Equations Using the Adomian Decomposition Method
Mon, 20 Jan 2014 06:48:33 +0000
http://www.hindawi.com/journals/tswj/2014/150483/
We apply Adomian decomposition method (ADM) for obtaining approximate series solution of Urysohn integral equations. The ADM provides a direct recursive scheme for solving such problems approximately. The approximations of the solution are obtained in the form of series with easily calculable components. Furthermore, we also discuss the convergence and error analysis of the ADM. Moreover, three numerical examples are included to demonstrate the accuracy and applicability of the method.
Randhir Singh, Gnaneshwar Nelakanti, and Jitendra Kumar
Copyright © 2014 Randhir Singh et al. All rights reserved.

On Generalization Based on Bi et al. Iterative Methods with EighthOrder Convergence for Solving Nonlinear Equations
Sun, 19 Jan 2014 12:22:31 +0000
http://www.hindawi.com/journals/tswj/2014/272949/
The primary goal of this work is to provide a general optimal threestep class of iterative methods based on the schemes designed by Bi et al. (2009). Accordingly, it requires four functional evaluations per
iteration with eighthorder convergence. Consequently, it satisfies Kung and Traub’s conjecture relevant to
construction optimal methods without memory. Moreover, some concrete methods of this class are shown
and implemented numerically, showing their applicability and efficiency.
Taher Lotfi, Alicia Cordero, Juan R. Torregrosa, Morteza Amir Abadi, and Maryam Mohammadi Zadeh
Copyright © 2014 Taher Lotfi et al. All rights reserved.

Modified Projection Algorithms for Solving the Split Equality Problems
Sun, 19 Jan 2014 11:58:25 +0000
http://www.hindawi.com/journals/tswj/2014/328787/
The split equality problem (SEP) has extraordinary utility and broad applicability in many areas of applied mathematics. Recently, Byrne and Moudafi (2013)
proposed a CQ algorithm for solving it. In this paper, we propose a modification for the CQ algorithm, which computes the stepsize adaptively and performs an additional projection step onto two halfspaces in each iteration. We further propose a relaxation scheme for the selfadaptive projection algorithm by using projections onto halfspaces instead of those onto the original convex sets, which is much more practical. Weak convergence results for both algorithms are analyzed.
QiaoLi Dong and Songnian He
Copyright © 2014 QiaoLi Dong and Songnian He. All rights reserved.

Fixed Points of Difference Operator of Meromorphic Functions
Sun, 19 Jan 2014 07:00:51 +0000
http://www.hindawi.com/journals/tswj/2014/103249/
Let f be a transcendental meromorphic function of order less than one. The authors prove that the exact difference has infinitely many fixed points, if and are Borel exceptional values (or Nevanlinna deficiency values) of f. These results extend the related results obtained by Chen and Shon.
Zhaojun Wu and Hongyan Xu
Copyright © 2014 Zhaojun Wu and Hongyan Xu. All rights reserved.

On Fractional Model Reference Adaptive Control
Thu, 16 Jan 2014 11:57:53 +0000
http://www.hindawi.com/journals/tswj/2014/521625/
This paper extends the conventional Model Reference Adaptive Control systems to fractional ones based on the theory of fractional calculus. A control law and an incommensurate fractional adaptation law are designed for the fractional plant and the fractional reference model. The stability and
tracking convergence are analyzed using the frequency distributed fractional integrator model and Lyapunov theory. Moreover, numerical simulations of
both linear and nonlinear systems are performed to exhibit the viability and effectiveness of the proposed methodology.
Bao Shi, Jian Yuan, and Chao Dong
Copyright © 2014 Bao Shi et al. All rights reserved.

Birkhoff Normal Forms and KAM Theory for GumowskiMira Equation
Thu, 16 Jan 2014 09:30:21 +0000
http://www.hindawi.com/journals/tswj/2014/819290/
By using the KAM theory we investigate the stability of equilibrium solutions of the GumowskiMira equation: , where , and we obtain the Birkhoff normal forms for this equation for different equilibrium solutions.
M. R. S. Kulenović, Z. Nurkanović, and E. Pilav
Copyright © 2014 M. R. S. Kulenović et al. All rights reserved.

Interpolation by Hankel Translates of a Basis Function: Inversion Formulas and Polynomial Bounds
Thu, 16 Jan 2014 09:11:05 +0000
http://www.hindawi.com/journals/tswj/2014/242750/
For , the authors have developed elsewhere a scheme for interpolation by Hankel translates of a basis function in certain spaces of continuous functions () depending on a weight . The functions and are connected through the distributional identity , where denotes the generalized Hankel transform of order . In this paper, we use the projection operators associated with an appropriate direct sum decomposition of the Zemanian space in order to derive explicit representations of the derivatives and their Hankel transforms, the former ones being valid when is restricted to a suitable interval for which is continuous. Here, denotes the th iterate of the Bessel differential operator if , while is the identity operator. These formulas, which can be regarded as inverses of generalizations of the equation , will allow us to get some polynomial bounds for such derivatives. Corresponding results are obtained for the members of the interpolation space .
Cristian Arteaga and Isabel Marrero
Copyright © 2014 Cristian Arteaga and Isabel Marrero. All rights reserved.

Generalizations on Some HermiteHadamard Type Inequalities for Differentiable Convex Functions with Applications to Weighted Means
Thu, 16 Jan 2014 06:44:35 +0000
http://www.hindawi.com/journals/tswj/2014/717164/
Some new HermiteHadamard type inequalities for differentiable convex functions were presented by Xi and Qi. In this paper, we present new generalizations on the XiQi inequalities.
Banyat Sroysang
Copyright © 2014 Banyat Sroysang. All rights reserved.

On Conformal Conic Mappings of Spherical Domains
Tue, 14 Jan 2014 12:51:36 +0000
http://www.hindawi.com/journals/tswj/2014/840280/
The problem of the generation of homogeneous grids for spherical domains is considered
in the class of conformal conic mappings. The equivalence between secant and tangent projections is shown and splitting the set of conformal conic mappings into equivalence classes is presented. The problem of minimization of the mapping factor variation is solved in the class of conformal conic mappings. Obtained results can be used in applied sciences, such as geophysical fluid dynamics and cartography, where the flattening of the Earth surface is required.
Andrei Bourchtein and Ludmila Bourchtein
Copyright © 2014 Andrei Bourchtein and Ludmila Bourchtein. All rights reserved.

Infinitely Many Weak Solutions of the Laplacian Equation with Nonlinear Boundary Conditions
Tue, 14 Jan 2014 06:31:41 +0000
http://www.hindawi.com/journals/tswj/2014/194310/
We study the following Laplacian equation with nonlinear boundary conditions:
and where is a bounded domain in with smooth boundary . We prove that the equation has infinitely many weak solutions by using the variant fountain theorem due to Zou (2001) and do not need to satisfy the or condition.
FengYun Lu and GuiQian Deng
Copyright © 2014 FengYun Lu and GuiQian Deng. All rights reserved.

Periodic Solutions for Nonlinear IntegroDifferential Systems with Piecewise Constant Argument
Sun, 12 Jan 2014 13:10:32 +0000
http://www.hindawi.com/journals/tswj/2014/514854/
We investigate the existence of the periodic solutions of a nonlinear integrodifferential system with piecewise alternately advanced and retarded argument of generalized type, in short DEPCAG; that is, the argument is a general step function. We consider the critical case, when associated linear homogeneous system admits nontrivial periodic solutions. Criteria of existence of periodic solutions of such equations are obtained. In the process we use Green’s function for periodic solutions and convert the given DEPCAG into an equivalent integral equation. Then we construct appropriate mappings and employ Krasnoselskii’s fixed point theorem to show the existence of a periodic solution of this type of nonlinear differential equations. We also use the contraction mapping principle to show the existence of a unique periodic solution. Appropriate examples are given to show the feasibility of our results.
KuoShou Chiu
Copyright © 2014 KuoShou Chiu. All rights reserved.

WellPosedness of Nonlocal Parabolic Differential Problems with Dependent Operators
Sun, 12 Jan 2014 07:13:55 +0000
http://www.hindawi.com/journals/tswj/2014/519814/
The nonlocal boundary value problem for the parabolic differential equation in an arbitrary Banach space with the dependent linear positive operator is investigated. The wellposedness of this problem is established in Banach spaces of all valued continuous functions on satisfying a Hölder condition with a weight . New Schauder type exact estimates in Hölder norms for the solution of two nonlocal boundary value problems for parabolic equations with dependent coefficients are established.
Allaberen Ashyralyev and Asker Hanalyev
Copyright © 2014 Allaberen Ashyralyev and Asker Hanalyev. All rights reserved.

On the Fourth Power Mean of the TwoTerm Exponential Sums
Sun, 12 Jan 2014 06:42:55 +0000
http://www.hindawi.com/journals/tswj/2014/724840/
The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind fourth power mean of twoterm exponential sums and give an interesting identity and asymptotic formula for it.
Han Zhang and Wenpeng Zhang
Copyright © 2014 Han Zhang and Wenpeng Zhang. All rights reserved.

The Convergence Study of the Homotopy Analysis Method for Solving Nonlinear VolterraFredholm Integrodifferential Equations
Sun, 12 Jan 2014 00:00:00 +0000
http://www.hindawi.com/journals/tswj/2014/465951/
We aim to study the convergence of the homotopy analysis method (HAM in short) for solving special nonlinear VolterraFredholm integrodifferential equations. The sufficient condition for the convergence of the method is briefly addressed. Some illustrative examples are also presented to demonstrate the validity and applicability of the technique. Comparison of the obtained results HAM with exact solution shows that the method is reliable and capable of providing analytic treatment for solving such equations.
Behzad Ghanbari
Copyright © 2014 Behzad Ghanbari. All rights reserved.

Solution of the Nonlinear Mixed VolterraFredholm Integral Equations by Hybrid of BlockPulse Functions and Bernoulli Polynomials
Sun, 12 Jan 2014 00:00:00 +0000
http://www.hindawi.com/journals/tswj/2014/413623/
A new numerical method for solving the nonlinear mixed VolterraFredholm integral equations is presented. This method is based upon hybrid functions approximation. The properties of hybrid functions consisting of blockpulse
functions and Bernoulli polynomials are presented. The operational matrices of
integration and product are given. These matrices are then utilized to reduce
the nonlinear mixed VolterraFredholm integral equations to the solution of algebraic
equations. Illustrative examples are included to demonstrate the validity
and applicability of the technique.
S. Mashayekhi, M. Razzaghi, and O. Tripak
Copyright © 2014 S. Mashayekhi et al. All rights reserved.

Analysis of Rattleback Chaotic Oscillations
Wed, 08 Jan 2014 12:03:05 +0000
http://www.hindawi.com/journals/tswj/2014/569386/
Rattleback is a canoeshaped object, already known from ancient times, exhibiting a nontrivial rotational behaviour. Although its shape looks symmetric, its kinematic behaviour seems to be asymmetric. When spun in one direction it normally rotates, but when it is spun in the other direction it stops rotating and oscillates until it finally starts rotating in the other direction. It has already been reported that those oscillations demonstrate chaotic characteristics. In this paper, rattleback’s chaotic dynamics are studied by applying Kane’s model for different sets of (experimentally decided) parameters, which correspond to three different experimental prototypes made of wax, gypsum, and leadsolder. The emerging chaotic behaviour in all three cases has been studied and evaluated by the related timeseries analysis and the calculation of the strange attractors’ invariant parameters.
Michael Hanias, Stavros G. Stavrinides, and Santo Banerjee
Copyright © 2014 Michael Hanias et al. All rights reserved.

Equivalent Conditions of Generalized Convex Fuzzy Mappings
Wed, 08 Jan 2014 09:52:16 +0000
http://www.hindawi.com/journals/tswj/2014/412534/
We obtain some equivalent conditions of (strictly) pseudoconvex and quasiconvex fuzzy mappings. These results will be useful to present some characterizations of solutions for fuzzy mathematical programming.
Xue Wen Liu and Dou He
Copyright © 2014 Xue Wen Liu and Dou He. All rights reserved.

Couple of the Variational Iteration Method and FractionalOrder Legendre Functions Method for Fractional Differential Equations
Sun, 05 Jan 2014 13:37:31 +0000
http://www.hindawi.com/journals/tswj/2014/928765/
We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractionalorder Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Blockpulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique.
Fukang Yin, Junqiang Song, Hongze Leng, and Fengshun Lu
Copyright © 2014 Fukang Yin et al. All rights reserved.

Weighted Multilinear Hardy Operators on Herz Type Spaces
Sun, 05 Jan 2014 08:16:48 +0000
http://www.hindawi.com/journals/tswj/2014/420408/
This paper focuses on the bounds of weighted multilinear Hardy operators on the product Herz spaces and the product MorreyHerz spaces, respectively. We present a sufficient condition on the weight function that guarantees weighted multilinear Hardy operators to be bounded on the product Herz spaces. And the condition is necessary under certain assumptions. Finally, we extend the obtained results to the product MorreyHerz spaces.
Shuli Gong, Zunwei Fu, and Bolin Ma
Copyright © 2014 Shuli Gong et al. All rights reserved.

The STransform of Distributions
Thu, 02 Jan 2014 16:14:44 +0000
http://www.hindawi.com/journals/tswj/2014/623294/
Parseval’s formula and inversion formula for the Stransform are given. A relation between the Stransform and pseudodifferential operators is obtained. The Stransform is studied on the spaces and .
Sunil Kumar Singh
Copyright © 2014 Sunil Kumar Singh. All rights reserved.

Stability Analysis of Distributed Order Fractional Chen System
Sun, 29 Dec 2013 18:16:39 +0000
http://www.hindawi.com/journals/tswj/2013/645080/
We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integerorder Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found
that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results.
H. Aminikhah, A. Refahi Sheikhani, and H. Rezazadeh
Copyright © 2013 H. Aminikhah et al. All rights reserved.

Coefficient Estimates for Initial TaylorMaclaurin Coefficients for a Subclass of Analytic and BiUnivalent Functions Defined by AlOboudi Differential Operator
Sun, 29 Dec 2013 11:54:09 +0000
http://www.hindawi.com/journals/tswj/2013/171039/
We introduce and investigate an interesting subclass of analytic and biunivalent functions in the open unit disk . For functions belonging to the class , we obtain estimates on the first two TaylorMaclaurin coefficients and .
Serap Bulut
Copyright © 2013 Serap Bulut. All rights reserved.

An IntervalValued Intuitionistic Fuzzy TOPSIS Method Based on an Improved Score Function
Wed, 25 Dec 2013 15:11:29 +0000
http://www.hindawi.com/journals/tswj/2013/879089/
This paper proposes an improved score function for the effective ranking order of intervalvalued intuitionistic fuzzy sets (IVIFSs) and an intervalvalued intuitionistic fuzzy TOPSIS method based on the score function to solve multicriteria decisionmaking problems in which all the preference information provided by decisionmakers is expressed as intervalvalued intuitionistic fuzzy decision matrices where each of the elements is characterized by IVIFS value and the information about criterion weights is known. We apply the proposed score function to calculate the separation measures of each alternative from the positive and negative ideal solutions to determine the relative closeness coefficients. According to the values of the closeness coefficients, the alternatives can be ranked and the most desirable one(s) can be selected in the decisionmaking process. Finally, two illustrative examples for multicriteria fuzzy decisionmaking problems of alternatives are used as a demonstration of the applications and the effectiveness of the proposed decisionmaking method.
Zhiyong Bai
Copyright © 2013 Zhiyong Bai. All rights reserved.

CottonType and Joint Invariants for Linear Elliptic Systems
Wed, 25 Dec 2013 08:32:29 +0000
http://www.hindawi.com/journals/tswj/2013/540705/
Cottontype invariants for a subclass of a system of two linear elliptic equations, obtainable from a complex base linear elliptic equation, are derived both by spliting of the corresponding complex Cotton invariants of the base complex equation and from the Laplacetype invariants of the system of linear hyperbolic equations equivalent to the system of linear elliptic equations via linear complex transformations of the independent variables. It is shown
that Cottontype invariants derived from these two approaches are identical. Furthermore, Cottontype and joint invariants for a general system of two linear elliptic equations are also obtained from the Laplacetype and joint invariants for a system of two linear hyperbolic equations equivalent to the system of linear elliptic equations by complex changes of the independent variables. Examples are presented to illustrate the results.
A. Aslam and F. M. Mahomed
Copyright © 2013 A. Aslam and F. M. Mahomed. All rights reserved.

Explicit Solutions of a GravityInduced Film Flow along a Convectively Heated Vertical Wall
Wed, 25 Dec 2013 07:55:33 +0000
http://www.hindawi.com/journals/tswj/2013/475939/
The gravitydriven film flow has been analyzed along a vertical
wall subjected to a convective boundary condition. The Boussinesq approximation is applied
to simplify the buoyancy term, and similarity transformations are used on the mathematical
model of the problem under consideration, to obtain a set of coupled ordinary differential
equations. Then the reduced equations are solved explicitly by using homotopy analysis
method (HAM). The resulting solutions are investigated for heat transfer effects on velocity
and temperature profiles.
Ammarah Raees and Hang Xu
Copyright © 2013 Ammarah Raees and Hang Xu. All rights reserved.

Multiple Solutions for Nonhomogeneous Neumann Differential Inclusion Problems by the Laplacian
Tue, 24 Dec 2013 15:56:35 +0000
http://www.hindawi.com/journals/tswj/2013/753262/
A class of nonlinear Neumann problems driven by Laplacian with
a nonsmooth locally Lipschitz potential (hemivariational inequality) was considered. The approach used in this paper
is the variational method for locally Lipschitz functions. More precisely, Weierstrass theorem and Mountain Pass
theorem are used to prove the existence of at least two nontrivial solutions.
QingMei Zhou
Copyright © 2013 QingMei Zhou. All rights reserved.

An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations
Sun, 22 Dec 2013 18:35:13 +0000
http://www.hindawi.com/journals/tswj/2013/837243/
We develop a highorder fixed point type method to approximate a multiple root. By using three functional evaluations per full cycle, a new class of fourthorder methods for this purpose is suggested and established. The methods from the class require the knowledge of the multiplicity. We also present a method in the absence of multiplicity for nonlinear equations. In order to attest the efficiency of the obtained methods, we employ numerical comparisons alongside obtaining basins of attraction to compare them in the complex plane according to their convergence speed and chaotic behavior.
Fazlollah Soleymani, Stanford Shateyi, and Gülcan Özkum
Copyright © 2013 Fazlollah Soleymani et al. All rights reserved.

The Oscillation on Solutions of Some Classes of Linear Differential Equations with Meromorphic Coefficients of Finite Order
Mon, 16 Dec 2013 09:07:23 +0000
http://www.hindawi.com/journals/tswj/2013/243873/
This paper considers the oscillation on
meromorphic solutions of the secondorder linear differential equations
with the form where is a meromorphic function
with order. We obtain some theorems which are the improvement
and generalization of the results given by Bank and Laine, Cao and
Li, Kinnunen, and others.
HongYan Xu, Jin Tu, and ZuXing Xuan
Copyright © 2013 HongYan Xu et al. All rights reserved.

Sufficient Condition on the Fractional Integral for the Convergence of a Function
Sun, 15 Dec 2013 16:17:45 +0000
http://www.hindawi.com/journals/tswj/2013/428428/
A sufficient condition on the fractional integral of the absolute value of a function is given in this paper, which allows to assure the convergence of the function to zero. This result can be useful to assure the convergence of a function when it is hard to know its exact evolution, but conditions on
its fractional integral can be stated.
Manuel A. DuarteMermoud, Norelys AguilaCamacho, and Javier A. Gallegos
Copyright © 2013 Manuel A. DuarteMermoud et al. All rights reserved.

Analysis of a FractionalOrder Couple Model with Acceleration in Feelings
Thu, 12 Dec 2013 16:56:23 +0000
http://www.hindawi.com/journals/tswj/2013/730736/
A fractionalorder nonlinear dynamical model of couple has been introduced. Upper bounds are obtained for a fractionalorder nonlinear dynamical model. Also different from other models, a model with the order 2α is discussed. We are expecting an acceleration in feelings; that is why we increase the order of the derivative between . Stability analysis of the fractionalorder nonlinear dynamical model of involving two persons is studied using the fractional RouthHurwitz criteria. By using stability analysis on fractionalorder system, we obtain sufficient condition on the parameters for the locally asymptotic stability of equilibrium points. Finally, numerical simulations are presented to verify the obtained results.
Ilknur Koca and Nuri Ozalp
Copyright © 2013 Ilknur Koca and Nuri Ozalp. All rights reserved.

New Result of Analytic Functions Related to Hurwitz Zeta Function
Thu, 12 Dec 2013 16:55:45 +0000
http://www.hindawi.com/journals/tswj/2013/475643/
By using a linear operator, we obtain some new results for a normalized analytic function f defined by means of the Hadamard product of Hurwitz zeta function. A class related to this function will be introduced and the properties will be discussed.
F. Ghanim and M. Darus
Copyright © 2013 F. Ghanim and M. Darus. All rights reserved.

Numerical Solution of Some Types of Fractional Optimal Control Problems
Mon, 09 Dec 2013 09:24:32 +0000
http://www.hindawi.com/journals/tswj/2013/306237/
We present two different approaches for the numerical solution of fractional optimal control problems (FOCPs) based on a spectral method using Chebyshev polynomials. The fractional derivative is described in the Caputo sense. The first approach follows the paradigm “optimize first, then discretize” and relies on the approximation of the necessary optimality conditions in terms of the associated Hamiltonian. In the second approach, the state equation is discretized first using the Clenshaw and Curtis scheme for the numerical integration of nonsingular functions followed by the RayleighRitz method to evaluate both the state and control variables. Two illustrative examples are included to demonstrate the validity and applicability of the suggested approaches.
Nasser Hassan Sweilam, Tamer Mostafa AlAjami, and Ronald H. W. Hoppe
Copyright © 2013 Nasser Hassan Sweilam et al. All rights reserved.

Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces
Sun, 08 Dec 2013 14:16:10 +0000
http://www.hindawi.com/journals/tswj/2013/591620/
In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, a.e. on , , , , (*), where is a closed subset in a Banach space , , , , is an upper semicontinuous setvalued mapping with convex values satisfying , , where , with , and . The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces.
Messaoud Bounkhel
Copyright © 2013 Messaoud Bounkhel. All rights reserved.

Active Joint Mechanism Driven by Multiple Actuators Made of Flexible Bags: A Proposal of Dual Structural Actuator
Thu, 05 Dec 2013 15:56:18 +0000
http://www.hindawi.com/journals/tswj/2013/128916/
An actuator is required to change its speed and
force depending on the situation. Using multiple actuators for
one driving axis is one of the possible solutions; however, there
is an associated problem of output power matching. This study
proposes a new active joint mechanism using multiple actuators.
Because the actuator is made of a flexible bag, it does not
interfere with other actuators when it is depressurized. The proposed
joint achieved coordinated motion of multiple actuators. This
report also discusses a new actuator which has dual cylindrical
structure. The cylinders are composed of flexible bags with
different diameters. The joint torque is estimated based on the
following factors: empirical formula for the flexible actuator
torque, geometric relationship between the joint and the actuator,
and the principle of virtual work. The prototype joint mechanism
achieves coordinated motion of multiple actuators for one axis.
With this motion, small inner actuator contributes high speed
motion, whereas large outer actuator generates high torque. The
performance of the prototype joint is examined by speed and
torque measurements. The joint showed about 30% efficiency
at 2.0 Nm load torque under 0.15 MPa air input.
Hitoshi Kimura, Takuya Matsuzaki, Mokutaro Kataoka, and Norio Inou
Copyright © 2013 Hitoshi Kimura et al. All rights reserved.

A Mathematical Model with Pulse Effect for Three Populations of the Giant Panda and Two Kinds of Bamboo
Thu, 05 Dec 2013 15:35:20 +0000
http://www.hindawi.com/journals/tswj/2013/137384/
A mathematical model for the relationship between the populations of giant pandas and two kinds of bamboo is established. We use the impulsive perturbations to take into account the effect of a sudden collapse of bamboo as a food source. We show that this system is uniformly bounded. Using the Floquet theory and comparison techniques of impulsive equations, we find conditions for the local and global stabilities of the giant pandafree periodic solution. Moreover, we obtain sufficient conditions for the system to be permanent. The results provide a theoretical basis for giant panda habitat protection.
Xiangyun Shi and Guohua Song
Copyright © 2013 Xiangyun Shi and Guohua Song. All rights reserved.

Asymptotic Bounds for the TimePeriodic Solutions to the Singularly Perturbed Ordinary Differential Equations
Wed, 04 Dec 2013 17:12:36 +0000
http://www.hindawi.com/journals/tswj/2013/301609/
The periodical in time problem for singularly perturbed second order linear ordinary differential equation is considered. The boundary layer behavior of the solution and its first and second derivatives have been established. An example supporting the theoretical analysis is presented.
Gabil M. Amiraliyev and Aysenur Ucar
Copyright © 2013 Gabil M. Amiraliyev and Aysenur Ucar. All rights reserved.

Global Dynamics of Certain Homogeneous SecondOrder Quadratic Fractional Difference Equation
Wed, 04 Dec 2013 12:06:13 +0000
http://www.hindawi.com/journals/tswj/2013/210846/
We investigate the basins of attraction of equilibrium points and minimal periodtwo solutions of the difference equation of the form where the parameters ,, and are positive numbers and the initial conditions and are arbitrary nonnegative numbers. The unique feature of this equation is the coexistence of an equilibrium solution and the minimal periodtwo solution both of which are locally asymptotically stable.
M. GarićDemirović, M. R. S. Kulenović, and M. Nurkanović
Copyright © 2013 M. GarićDemirović et al. All rights reserved.

Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions
Thu, 28 Nov 2013 18:17:47 +0000
http://www.hindawi.com/journals/tswj/2013/567132/
We apply generalized operators of fractional integration involving Appell’s function due to MarichevSaigoMaeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, ErdélyiKober, RiemannLiouville, and Weyl type of fractional integrals are also presented. Some interesting special cases of our two main results are presented. We also point out that the results presented here, being of general character, are easily reducible to yield many diverse new and known integral formulas involving simpler functions.
D. Baleanu, P. Agarwal, and S. D. Purohit
Copyright © 2013 D. Baleanu et al. All rights reserved.

On the Approximation of Generalized Lipschitz Function by Euler Means of Conjugate Series of Fourier Series
Tue, 26 Nov 2013 11:29:34 +0000
http://www.hindawi.com/journals/tswj/2013/508026/
Approximation theory is a very important field which has various applications in pure and applied mathematics. The present study deals with a new theorem on the approximation of functions of Lipschitz class by using Euler’s mean of conjugate series of Fourier series. In this paper, the degree of approximation by using Euler’s means of conjugate of functions belonging to class has been obtained. and classes are the particular cases of class. The main result of this paper generalizes some wellknown results in this direction.
Jitendra Kumar Kushwaha
Copyright © 2013 Jitendra Kumar Kushwaha. All rights reserved.

DaveyStewartson Equation with Fractional Coordinate Derivatives
Mon, 25 Nov 2013 17:05:18 +0000
http://www.hindawi.com/journals/tswj/2013/941645/
We have used the homotopy analysis method (HAM) to obtain solution of DaveyStewartson equations
of fractional order. The fractional derivative is described in the Caputo sense. The results obtained by this method have
been compared with the exact solutions. Stability and convergence of the proposed approach is investigated. The effects of
fractional derivatives for the systems under consideration are discussed. Furthermore, comparisons indicate that there is a very good agreement between the solutions of homotopy analysis method and the exact solutions in terms of accuracy.
H. Jafari, K. Sayevand, Yasir Khan, and M. Nazari
Copyright © 2013 H. Jafari et al. All rights reserved.

The Exact Distribution of the Condition Number of Complex Random Matrices
Mon, 25 Nov 2013 11:47:20 +0000
http://www.hindawi.com/journals/tswj/2013/729839/
Let be a complex random matrix and which is the complex Wishart matrix. Let and denote the eigenvalues of the W and singular values of , respectively. The 2norm condition number of is . In this paper, the exact distribution of the condition number of the complex Wishart matrices is derived. The distribution is expressed in terms of complex zonal polynomials.
Lin Shi, Taibin Gan, Hong Zhu, and Xianming Gu
Copyright © 2013 Lin Shi et al. All rights reserved.

Drawing Dynamical and Parameters Planes of Iterative Families and Methods
Sun, 24 Nov 2013 13:42:40 +0000
http://www.hindawi.com/journals/tswj/2013/780153/
The complex dynamical analysis of the parametric fourthorder Kim’s iterative family is made on quadratic polynomials, showing the MATLAB codes generated to draw the fractal images necessary to complete the study. The parameter spaces associated with the free critical points have been analyzed, showing the stable (and unstable) regions where the selection of the parameter will provide us the excellent schemes (or dreadful ones).
Francisco I. Chicharro, Alicia Cordero, and Juan R. Torregrosa
Copyright © 2013 Francisco I. Chicharro et al. All rights reserved.

Strong Convergence of a Monotone Projection Algorithm in a Banach Space
Thu, 21 Nov 2013 11:32:50 +0000
http://www.hindawi.com/journals/tswj/2013/764909/
In this paper, a common solution problem is investigated based on a Bregman projection. Strong convergence of the monotone projection algorithm for monotone operators and bifunctions is obtained in a reflexive Banach space.
Songtao Lv
Copyright © 2013 Songtao Lv. All rights reserved.

Dynamic Behavior for an SIRS Model with Nonlinear Incidence Rate and Treatment
Thu, 21 Nov 2013 11:00:19 +0000
http://www.hindawi.com/journals/tswj/2013/209256/
This paper considers an SIRS model with nonlinear incidence rate and treatment. It is assumed that susceptible and infectious individuals have constant immigration rates. We investigate the existence of equilibrium and prove the global asymptotical stable results of the endemic equilibrium. We then obtained that the model undergoes a Hopf bifurcation and existences a limit cycle. Some numerical simulations are given to illustrate the analytical results.
Junhong Li and Ning Cui
Copyright © 2013 Junhong Li and Ning Cui. All rights reserved.

Some New Generalized Difference Spaces of Nonabsolute Type Derived from the Spaces and
Thu, 14 Nov 2013 18:56:02 +0000
http://www.hindawi.com/journals/tswj/2013/349346/
We introduce the sequence space of none absolute type which is a normed space and space in the cases and , respectively, and prove that and are linearly isomorphic for . Furthermore, we give some inclusion relations concerning the space and we construct the basis for the space , where . Furthermore, we determine the alpha, beta and gammaduals of the space for . Finally, we investigate some geometric properties concerning BanachSaks type and give Gurarii's modulus of convexity for the normed space .
Feyzi Başar and Ali Karaisa
Copyright © 2013 Feyzi Başar and Ali Karaisa. All rights reserved.

Positive Periodic Solutions of an Epidemic Model with Seasonality
Sun, 10 Nov 2013 14:35:43 +0000
http://www.hindawi.com/journals/tswj/2013/470646/
An SEI autonomous model with logistic growth rate and its corresponding nonautonomous model are investigated. For the autonomous case, we give the attractive regions of equilibria and perform some numerical simulations. Basic demographic reproduction number is obtained. Moreover, only the basic reproduction number cannot ensure the existence of the positive equilibrium, which needs additional condition . For the nonautonomous case, by introducing the basic reproduction number defined by the spectral radius, we study the uniform persistence and extinction of the disease. The results show that for the periodic system the basic reproduction number is more accurate than the average reproduction number.
GuiQuan Sun, Zhenguo Bai, ZiKe Zhang, Tao Zhou, and Zhen Jin
Copyright © 2013 GuiQuan Sun et al. All rights reserved.

An Expansion Formula with HigherOrder Derivatives for Fractional Operators of Variable Order
Sun, 10 Nov 2013 09:44:31 +0000
http://www.hindawi.com/journals/tswj/2013/915437/
We obtain approximation formulas for fractional integrals and derivatives of RiemannLiouville and Marchaud types with a variable fractional order. The approximations involve integerorder derivatives only. An estimation for the error is given. The efficiency of the approximation method is illustrated with examples. As applications, we show how the obtained results are useful to solve differential equations, and problems of the calculus of variations that depend on fractional derivatives of Marchaud type.
Ricardo Almeida and Delfim F. M. Torres
Copyright © 2013 Ricardo Almeida and Delfim F. M. Torres. All rights reserved.

Multiple Positive Solutions for Nonlinear Fractional Boundary Value Problems
Wed, 06 Nov 2013 17:28:12 +0000
http://www.hindawi.com/journals/tswj/2013/473828/
This paper is devoted to the existence of multiple positive solutions for fractional boundary value problem , , , where is a real number, is the Caputo fractional derivative, and is continuous. Firstly, by constructing a special cone, applying GuoKrasnoselskii’s fixed point theorem and LeggettWilliams fixed point theorem, some new existence criteria for fractional boundary value problem are established; secondly, by applying a new extension of Krasnoselskii’s fixed point theorem, a sufficient condition is obtained for the existence of multiple positive solutions to the considered boundary value problem from its auxiliary problem. Finally, as applications, some illustrative examples are presented to support the main results.
Daliang Zhao and Yansheng Liu
Copyright © 2013 Daliang Zhao and Yansheng Liu. All rights reserved.

Nonuniform Exponential Dichotomies in Terms of Lyapunov Functions for Noninvertible Linear DiscreteTime Systems
Wed, 06 Nov 2013 15:10:47 +0000
http://www.hindawi.com/journals/tswj/2013/901026/
The aim of this paper is to give characterizations in terms of Lyapunov functions for nonuniform exponential dichotomies of nonautonomous and noninvertible discretetime systems.
IoanLucian Popa, Mihail Megan, and Traian Ceauşu
Copyright © 2013 IoanLucian Popa et al. All rights reserved.

Locally Expansive Solutions for a Class of Iterative Equations
Tue, 05 Nov 2013 17:17:50 +0000
http://www.hindawi.com/journals/tswj/2013/372681/
Iterative equations which can be expressed by the following form , where , are investigated. Conditions for the existence of locally expansive solutions for such equations are given.
Wei Song and Sheng Chen
Copyright © 2013 Wei Song and Sheng Chen. All rights reserved.

KorovkinType Theorems in Weighted Spaces via Summation Process
Tue, 05 Nov 2013 15:28:06 +0000
http://www.hindawi.com/journals/tswj/2013/534054/
Korovkintype theorem which is one of the fundamental methods in
approximation theory to describe uniform convergence of any sequence of
positive linear operators is discussed on weighted spaces, for univariate and multivariate functions, respectively.
Furthermore, we obtain these types of approximation theorems by means of summability which is a stronger convergence method than
ordinary convergence.
Tuncer Acar and Fadime Dirik
Copyright © 2013 Tuncer Acar and Fadime Dirik. All rights reserved.

Some Endpoint Results for βGeneralized Weak Contractive Multifunctions
Mon, 04 Nov 2013 08:42:22 +0000
http://www.hindawi.com/journals/tswj/2013/948472/
We introduce βgeneralized weak contractive multifunctions and give some
results about endpoints of the multifunctions. Also, we give some results about role of a
point in the existence of endpoints.
H. Alikhani, D. Gopal, M. A. Miandaragh, Sh. Rezapour, and N. Shahzad
Copyright © 2013 H. Alikhani et al. All rights reserved.

Multiple Solutions for a Class of Dirichlet Double Eigenvalue Quasilinear Elliptic Systems Involving the ()Laplacian Operator
Sun, 03 Nov 2013 13:19:22 +0000
http://www.hindawi.com/journals/tswj/2013/767989/
Existence results of three weak solutions for a Dirichlet double eigenvalue quasilinear elliptic system involving the ()Laplacian operator, under suitable assumptions, are established. Our main tool is based on a recent threecriticalpoint theorem obtained by Ricceri. We also give some examples to illustrate the obtained results.
Armin Hadjian and Saleh Shakeri
Copyright © 2013 Armin Hadjian and Saleh Shakeri. All rights reserved.

Some New Inequalities of Jordan Type for Sine
Thu, 31 Oct 2013 12:00:14 +0000
http://www.hindawi.com/journals/tswj/2013/834159/
The authors find some new inequalities of Jordan type for the sine function. These newly established inequalities are of new form and are applied to deduce some known results.
ShanPeng Zeng and YueSheng Wu
Copyright © 2013 ShanPeng Zeng and YueSheng Wu. All rights reserved.

Monotonicity, Concavity, and Convexity of Fractional Derivative of Functions
Thu, 31 Oct 2013 11:20:48 +0000
http://www.hindawi.com/journals/tswj/2013/605412/
The monotonicity of the solutions of a class of nonlinear fractional differential equations is studied first, and the existing results were extended. Then we discuss monotonicity, concavity, and convexity of fractional derivative of some functions and derive corresponding criteria. Several examples are provided to illustrate the applications of our results.
XianFeng Zhou, Song Liu, Zhixin Zhang, and Wei Jiang
Copyright © 2013 XianFeng Zhou et al. All rights reserved.

On Harmonic Meromorphic Functions Associated with Basic Hypergeometric Functions
Thu, 31 Oct 2013 09:34:28 +0000
http://www.hindawi.com/journals/tswj/2013/164287/
By making use of basic hypergeometric functions, a class of complex harmonic meromorphic functions with positive coefficients is introduced. We obtain some properties such as coefficient inequality,
growth theorems, and extreme points.
Huda Al dweby and Maslina Darus
Copyright © 2013 Huda Al dweby and Maslina Darus. All rights reserved.

Certain Subclasses of Analytic Functions with Complex Order
Tue, 29 Oct 2013 10:20:29 +0000
http://www.hindawi.com/journals/tswj/2013/958796/
Two new subclasses of analytic functions of complex order are introduced. Apart from establishing coefficient bounds for these classes, we establish inclusion relationships involving () neighborhoods of analytic functions with negative coefficients belonging to these subclasses.
A. Selvam, P. Sooriya Kala, and N. Marikkannan
Copyright © 2013 A. Selvam et al. All rights reserved.

ViscosityProjection Method for a Family of General Equilibrium Problems and Asymptotically Strict Pseudocontractions in the Intermediate Sense
Mon, 28 Oct 2013 14:10:25 +0000
http://www.hindawi.com/journals/tswj/2013/608241/
In this paper, a MeirKeeler contraction is introduced to propose a viscosityprojection approximation method for finding a common element of the set of solutions of a family of general equilibrium problems and the set of fixed points of asymptotically strict pseudocontractions in the intermediate sense. Strong convergence of the viscosity iterative sequences is obtained under some suitable conditions. Results presented in this paper extend and unify the previously known results announced by many other authors.
DaoJun Wen
Copyright © 2013 DaoJun Wen. All rights reserved.

On the Stability of OneDimensional Wave Equation
Sun, 27 Oct 2013 16:14:03 +0000
http://www.hindawi.com/journals/tswj/2013/978754/
We prove the generalized HyersUlam stability of the onedimensional wave equation, , in a class of twice continuously differentiable functions.
SoonMo Jung
Copyright © 2013 SoonMo Jung. All rights reserved.

Multiple Solutions for a Singular Quasilinear Elliptic System
Thu, 24 Oct 2013 14:07:34 +0000
http://www.hindawi.com/journals/tswj/2013/278013/
We consider the multiplicity of nontrivial solutions of the following quasilinear elliptic system , , , , , where , , , , , . The functions , , , , , , and
satisfy some suitable conditions. We will prove that the problem has at least two nontrivial solutions by using Mountain Pass Theorem and Ekeland's variational principle.
Lin Chen, Caisheng Chen, and Zonghu Xiu
Copyright © 2013 Lin Chen et al. All rights reserved.

Incomplete Augmented Lagrangian Preconditioner for Steady Incompressible NavierStokes Equations
Tue, 22 Oct 2013 15:59:08 +0000
http://www.hindawi.com/journals/tswj/2013/486323/
An incomplete augmented Lagrangian preconditioner, for the steady incompressible NavierStokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangianbased preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.
NingBo Tan, TingZhu Huang, and ZeJun Hu
Copyright © 2013 NingBo Tan et al. All rights reserved.

Bounds for Combinations of Toader Mean and Arithmetic Mean in Terms of Centroidal Mean
Tue, 22 Oct 2013 15:17:14 +0000
http://www.hindawi.com/journals/tswj/2013/842542/
The authors find the greatest value and the least value , such that the double inequality holds for all and with , where , , and denote, respectively, the centroidal, arithmetic, and Toader means of the two positive numbers and .
WeiDong Jiang
Copyright © 2013 WeiDong Jiang. All rights reserved.

An Efficient Method for Systems of Variable Coefficient Coupled Burgers’ Equation with TimeFractional Derivative
Thu, 10 Oct 2013 18:48:31 +0000
http://www.hindawi.com/journals/tswj/2013/687695/
A new homotopy perturbation method (NHPM) is applied to system of variable coefficient coupled Burgers' equation with timefractional derivative. The fractional derivatives are described in the Caputo fractional derivative sense. The concept of new algorithm is introduced briefly, and NHPM is examined for two systems of nonlinear Burgers' equation. In this approach, the solution is considered as a power series expansion that converges rapidly to the nonlinear problem. The new approximate analytical procedure depends on two iteratives. The modified algorithm provides approximate solutions in the form of convergent series with easily computable components. Results indicate that the introduced method is promising for solving other types of systems of nonlinear fractionalorder partial differential equations.
Hossein Aminikhah and Nasrin Malekzadeh
Copyright © 2013 Hossein Aminikhah and Nasrin Malekzadeh. All rights reserved.

Inclusions in a Single Variable in Ultrametric Spaces and HyersUlam Stability
Tue, 01 Oct 2013 15:45:35 +0000
http://www.hindawi.com/journals/tswj/2013/129637/
We present some properties of setvalued inclusions in a single variable
in ultrametric spaces. As a consequence, we obtain stability results
for the corresponding functional equations.
Magdalena Piszczek
Copyright © 2013 Magdalena Piszczek. All rights reserved.

A Higher Order Iterative Method for Computing the Drazin Inverse
Mon, 30 Sep 2013 15:33:46 +0000
http://www.hindawi.com/journals/tswj/2013/708647/
A method with high convergence rate for finding approximate inverses of nonsingular matrices is suggested
and established analytically. An extension of the introduced computational scheme to general square matrices is
defined. The extended method could be used for finding the Drazin inverse. The application of the scheme on large sparse test matrices alongside the use in preconditioning of linear system of equations will be presented to clarify the contribution of the paper.
F. Soleymani and Predrag S. Stanimirović
Copyright © 2013 F. Soleymani and Predrag S. Stanimirović. All rights reserved.

Trichotomy for Dynamical Systems in Banach Spaces
Sun, 29 Sep 2013 14:55:53 +0000
http://www.hindawi.com/journals/tswj/2013/793813/
We construct a framework for the study of dynamical systems that describe phenomena from physics and engineering in infinite dimensions and whose state evolution is set out by skewevolution semiflows. Therefore, we introduce the concept of trichotomy. Characterizations in a uniform setting are proved, using techniques from the
domain of nonautonomous evolution equations with unbounded coefficients, and connections with the classic notion of trichotomy are given. The statements are sustained by several examples.
Codruţa Stoica
Copyright © 2013 Codruţa Stoica. All rights reserved.

Controllability in Hybrid Kinetic Equations Modeling Nonequilibrium Multicellular Systems
Thu, 26 Sep 2013 15:30:03 +0000
http://www.hindawi.com/journals/tswj/2013/274719/
This paper is concerned with the derivation of hybrid kinetic partial integrodifferential equations that can be proposed for the mathematical modeling of multicellular systems subjected to external force fields and characterized by nonconservative interactions. In order to prevent an uncontrolled time evolution of the moments of the solution, a control operator is introduced which is based on the Gaussian thermostat. Specifically, the analysis shows that the moments are solution of a Riccatitype differential equation.
Carlo Bianca
Copyright © 2013 Carlo Bianca. All rights reserved.

New Criteria for Functions to Be in a Class of Valent Alpha Convex Functions
Thu, 26 Sep 2013 09:03:10 +0000
http://www.hindawi.com/journals/tswj/2013/280191/
We obtain certain simple sufficiency criteria for a class of valent alpha convex functions. Many known results appear as special consequences of our work. Some applications of our work to the generalized integral operator are also given.
Muhammad Arif, Muhammad Ayaz, and Mohamed Kamal Aouf
Copyright © 2013 Muhammad Arif et al. All rights reserved.

Taylor’s Expansion for Composite Functions
Wed, 25 Sep 2013 14:26:12 +0000
http://www.hindawi.com/journals/tswj/2013/536280/
We build a Taylor’s expansion for composite functions. Some applications are introduced, where the proposed technique allows the authors to obtain an asymptotic expansion of high order in many small parameters of solutions.
Le Thi Phuong Ngoc and Nguyen Anh Triet
Copyright © 2013 Le Thi Phuong Ngoc and Nguyen Anh Triet. All rights reserved.

Existence and Uniqueness of Solution for a Class of Stochastic Differential Equations
Thu, 19 Sep 2013 17:13:17 +0000
http://www.hindawi.com/journals/tswj/2013/132923/
A class of stochastic differential equations given by , , , are investigated. Upon making some suitable assumptions, the existence and uniqueness of solution for the equations are obtained. Moreover, the existence and uniqueness of solution
for stochastic Lorenz system, which is illustrated by example, are in good agreement with the theoretical analysis.
Junfei Cao, Zaitang Huang, and Caibin Zeng
Copyright © 2013 Junfei Cao et al. All rights reserved.

Dual Synchronization of FractionalOrder Chaotic Systems via a Linear Controller
Sat, 14 Sep 2013 08:39:56 +0000
http://www.hindawi.com/journals/tswj/2013/159194/
The problem of the dual synchronization of two different fractionalorder chaotic systems is studied. By a linear controller, we realize the dual synchronization of fractionalorder chaotic systems. Finally, the proposed method is applied for dual synchronization of Van der PolWillis systems and Van der PolDuffing systems. The numerical simulation shows the accuracy of the theory.
Jian Xiao, Zhenzhen Ma, and Yehong Yang
Copyright © 2013 Jian Xiao et al. All rights reserved.

Solving Fuzzy Fractional Differential Equations Using Zadeh's Extension Principle
Wed, 04 Sep 2013 10:37:09 +0000
http://www.hindawi.com/journals/tswj/2013/454969/
We study a fuzzy fractional differential equation (FFDE) and
present its solution using Zadeh’s extension principle. The proposed study extends the
case of fuzzy differential equations of integer order. We also propose a numerical method
to approximate the solution of FFDEs. To solve nonlinear problems, the proposed
numerical method is then incorporated into an unconstrained optimisation technique. Several
numerical examples are provided.
M. Z. Ahmad, M. K. Hasan, and S. Abbasbandy
Copyright © 2013 M. Z. Ahmad et al. All rights reserved.

Positive Solutions of Advanced Differential Systems
Sat, 31 Aug 2013 15:15:44 +0000
http://www.hindawi.com/journals/tswj/2013/613832/
We study asymptotic behavior of solutions of general advanced differential systems , where is a continuous quasibounded functional which satisfies a local Lipschitz
condition with respect to the second argument and is a subset in , ,
, and , . A monotone iterative method is proposed to prove
the existence of a solution defined for with the graph coordinates lying between
graph coordinates of two (lower and upper) auxiliary vector functions. This result is applied to scalar advanced linear differential equations. Criteria of existence of positive solutions are given and their asymptotic behavior is discussed.
Josef Diblík and Mária Kúdelčíková
Copyright © 2013 Josef Diblík and Mária Kúdelčíková. All rights reserved.

On the Normed Space of Equivalence Classes of Fuzzy Numbers
Thu, 29 Aug 2013 11:40:42 +0000
http://www.hindawi.com/journals/tswj/2013/792484/
We study the norm induced by the supremum metric on the space of fuzzy numbers. And then we propose a method for constructing a norm on the quotient space of fuzzy numbers. This norm is very natural and works well with the induced metric on the quotient space.
Dong Qiu, Chongxia Lu, and Wei Zhang
Copyright © 2013 Dong Qiu et al. All rights reserved.

Fixed Point Results of Locally Contractive Mappings in Ordered QuasiPartial Metric Spaces
Sun, 25 Aug 2013 10:59:30 +0000
http://www.hindawi.com/journals/tswj/2013/194897/
Fixed point results for a selfmap satisfying locally contractive conditions on a closed ball in an ordered 0complete quasipartial metric space have
been established. Instead of monotone mapping, the notion of dominated mappings is applied. We have used weaker metric, weaker contractive conditions, and
weaker restrictions to obtain unique fixed points. An example is given which shows that how this result can be used when the corresponding results cannot. Our results generalize, extend, and improve several wellknown conventional results.
Abdullah Shoaib, Muhammad Arshad, and Jamshaid Ahmad
Copyright © 2013 Abdullah Shoaib et al. All rights reserved.

Oscillation of a Class of Fractional Differential Equations with Damping Term
Wed, 21 Aug 2013 10:34:50 +0000
http://www.hindawi.com/journals/tswj/2013/685621/
We investigate the oscillation of a class of fractional differential equations with damping term.
Based on a certain variable transformation, the fractional differential equations are converted into another
differential equations of integer order with respect to the new variable. Then, using Riccati transformation,
inequality, and integration average technique, some new oscillatory criteria for the equations are established.
As for applications, oscillation for two certain fractional differential equations with damping term is investigated by the use of the presented results.
Huizeng Qin and Bin Zheng
Copyright © 2013 Huizeng Qin and Bin Zheng. All rights reserved.

On Generalized Carleson Operators of Periodic Wavelet Packet Expansions
Tue, 20 Aug 2013 13:07:26 +0000
http://www.hindawi.com/journals/tswj/2013/379861/
Three new theorems based on the generalized Carleson operators for the periodic Walshtype wavelet packets have been established. An application of these theorems as convergence a.e. for the periodic Walshtype wavelet packet expansion of block function with the help of summation by arithmetic means has been studied.
Shyam Lal and Manoj Kumar
Copyright © 2013 Shyam Lal and Manoj Kumar. All rights reserved.

Fractional Solutions of Bessel Equation with Method
Mon, 19 Aug 2013 09:40:01 +0000
http://www.hindawi.com/journals/tswj/2013/685695/
This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the fractional calculus operator method, we derive the fractional solutions of the equation.
Erdal Bas, Resat Yilmazer, and Etibar Panakhov
Copyright © 2013 Erdal Bas et al. All rights reserved.

Nonoscillatory Central Schemes for Hyperbolic Systems of Conservation Laws in ThreeSpace Dimensions
Sun, 18 Aug 2013 12:00:21 +0000
http://www.hindawi.com/journals/tswj/2013/672187/
We extend a family of highresolution, semidiscrete central schemes for hyperbolic systems of conservation laws to threespace dimensions. Details of the schemes, their implementation, and properties are presented together with results from several prototypical applications of hyperbolic conservation laws including a nonlinear scalar equation, the Euler equations of gas dynamics, and the ideal magnetohydrodynamic equations. Parallel scaling analysis and gridindependent results including contours and isosurfaces of density and velocity and magnetic field vectors are shown in this study, confirming the ability of these types of solvers to approximate the solutions of hyperbolic equations efficiently and accurately.
Andrew N. Guarendi and Abhilash J. Chandy
Copyright © 2013 Andrew N. Guarendi and Abhilash J. Chandy. All rights reserved.

Exceptional Values of Meromorphic Function on Annulus
Mon, 05 Aug 2013 10:19:41 +0000
http://www.hindawi.com/journals/tswj/2013/937584/
The main purpose of this paper is to study the exceptional values of meromorphic function and its derivative on annulus. We also give some theorems and corollaries about exceptional values of meromorphic function on the annulus, which are the improvement of the previous results given by Chen and Wu.
HongYan Xu
Copyright © 2013 HongYan Xu. All rights reserved.

On the Connection Coefficients of the ChebyshevBoubaker Polynomials
Sun, 04 Aug 2013 11:49:02 +0000
http://www.hindawi.com/journals/tswj/2013/657806/
The ChebyshevBoubaker polynomials are the orthogonal polynomials whose coefficient arrays are defined by ordinary Riordan arrays. Examples include the Chebyshev polynomials of the second kind and the Boubaker polynomials. We study the connection coefficients of this class of orthogonal polynomials, indicating how Riordan array techniques can lead to closedform expressions for these connection coefficients as well as recurrence relations that define them.
Paul Barry
Copyright © 2013 Paul Barry. All rights reserved.

Existence of Multiple Solutions for a Kirchhoff Problem with Nonlinear Boundary Conditions
Thu, 25 Jul 2013 14:17:19 +0000
http://www.hindawi.com/journals/tswj/2013/516093/
The paper considers the existence of multiple solutions of the singular nonlocal elliptic problem , , = , on , where , . By the variational method on the Nehari manifold, we prove that the problem has at least two positive solutions when some conditions are satisfied.
Zonghu Xiu and Caisheng Chen
Copyright © 2013 Zonghu Xiu and Caisheng Chen. All rights reserved.

On Weak Exponential Expansiveness of Evolution Families in Banach Spaces
Thu, 25 Jul 2013 14:06:35 +0000
http://www.hindawi.com/journals/tswj/2013/284630/
The aim of this paper is to give several characterizations for the property of weak exponential expansiveness for evolution families in Banach spaces. Variants for weak exponential expansiveness of some wellknown results in stability theory (Datko (1973), Rolewicz (1986), Ichikawa (1984), and Megan et al. (2003)) are obtained.
Tian Yue, Xiaoqiu Song, and Dongqing Li
Copyright © 2013 Tian Yue et al. All rights reserved.

On thOrder Slant Weighted Toeplitz Operator
Wed, 17 Jul 2013 08:34:42 +0000
http://www.hindawi.com/journals/tswj/2013/960853/
Let be a sequence of positive numbers with , when and when . A thorder slant weighted Toeplitz operator on is given by , where is the multiplication on and is an operator on given by , being the orthonormal basis for . In this paper, we define a thorder slant weighted Toeplitz matrix and characterise in terms of this matrix. We further prove some properties of using this characterisation.
S. C. Arora and Ritu Kathuria
Copyright © 2013 S. C. Arora and Ritu Kathuria. All rights reserved.

On SatnoianuWu’s Inequality
Tue, 16 Jul 2013 14:27:20 +0000
http://www.hindawi.com/journals/tswj/2013/645201/
By applying techniques in the theory of convex functions and Schurgeometrically convex functions, the author investigates a conjecture of Satnoianu on an algebraic inequality and generalizes some known results in recent years.
BoYan Xi
Copyright © 2013 BoYan Xi. All rights reserved.

On a Family of Multivariate Modified Humbert Polynomials
Sun, 14 Jul 2013 12:24:30 +0000
http://www.hindawi.com/journals/tswj/2013/187452/
This paper attempts to present a multivariable extension of generalized Humbert polynomials. The results obtained here include various families of multilinear and multilateral generating functions, miscellaneous properties, and also some special cases for these multivariable polynomials.
Rabia Aktaş and Esra ErkuşDuman
Copyright © 2013 Rabia Aktaş and Esra ErkuşDuman. All rights reserved.