Abstract and Applied Analysis http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Certain Inequalities Involving the Fractional -Integral Operators Wed, 23 Apr 2014 14:46:13 +0000 http://www.hindawi.com/journals/aaa/2014/371274/ We establish some inequalities involving Saigo fractional -integral operator in the theory of quantum calculus by using the two parameters of deformation, and , whose special cases are shown to yield corresponding inequalities associated with Riemann-Liouville and Kober fractional -integral operators, respectively. Furthermore, we also consider their relevance with other related known results. Dumitru Baleanu and Praveen Agarwal Copyright © 2014 Dumitru Baleanu and Praveen Agarwal. All rights reserved. Modeling Peer-to-Peer Botnet on Scale-Free Network Wed, 23 Apr 2014 13:47:19 +0000 http://www.hindawi.com/journals/aaa/2014/212478/ Peer-to-peer (P2P) botnets have emerged as one of the serious threats to Internet security. To prevent effectively P2P botnet, in this paper, a mathematical model which combines the scale-free trait of Internet with the formation of P2P botnet is presented. Explicit mathematical analysis demonstrates that the model has a globally stable endemic equilibrium when infection rate is greater than a critical value. Meanwhile, we find that, in scale-free network, the critical value is very little. Hence, it is unrealistic to completely dispel the P2P botnet. Numerical simulations show that one can take effective countermeasures to reduce the scale of P2P botnet or delay its outbreak. Our findings can provide meaningful instruction to network security management. Liping Feng, Hongbin Wang, Qi Han, Qingshan Zhao, and Lipeng Song Copyright © 2014 Liping Feng et al. All rights reserved. Conservation Laws and Traveling Wave Solutions of a Generalized Nonlinear ZK-BBM Equation Wed, 23 Apr 2014 13:42:56 +0000 http://www.hindawi.com/journals/aaa/2014/139513/ We study a generalized two-dimensional nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM) equation, which is in fact Benjamin-Bona-Mahony equation formulated in the ZK sense. Conservation laws for this equation are constructed by using the new conservation theorem due to Ibragimov and the multiplier method. Furthermore, traveling wave solutions are obtained by employing the -expansion method. Khadijo Rashid Adem and Chaudry Masood Khalique Copyright © 2014 Khadijo Rashid Adem and Chaudry Masood Khalique. All rights reserved. Predictive Function Optimization Control for a Class of Hydraulic Servo Vibration Systems Wed, 23 Apr 2014 11:45:55 +0000 http://www.hindawi.com/journals/aaa/2014/750851/ This paper is concerned with the problem of predictive function control (PFC) for a class of hydraulic vibration servo control systems. Our aim is to design a new advanced control strategy such that the control system can track trajectory in a fast and accurate way. For this end, the mathematical model of the hydraulic vibration servo control system is firstly studied. By analyzing the nonlinear, time-varying, and model structure uncertainty features of the objects, the desired control strategy is presented based on PFC. Finally, the simulation results show that our proposed method is effective and can be used to improve the tracking speed, accuracy, and robustness. Xugang Feng, Jiayan Zhang, Jing Wang, Shaokang Xiong, Qiling Wu, and Yetai Fei Copyright © 2014 Xugang Feng et al. All rights reserved. Multiplicity of Periodic Solutions for a Higher Order Difference Equation Wed, 23 Apr 2014 09:03:16 +0000 http://www.hindawi.com/journals/aaa/2014/925290/ We study a higher order difference equation. By Lyapunov-Schmidt reduction methods and computations of critical groups, we prove that the equation has four -periodic solutions. Ronghui Hu Copyright © 2014 Ronghui Hu. All rights reserved. Feller Property for a Special Hybrid Jump-Diffusion Model Wed, 23 Apr 2014 08:59:26 +0000 http://www.hindawi.com/journals/aaa/2014/412848/ We consider the stochastic stability for a hybrid jump-diffusion model, where the switching here is a phase semi-Markovian process. We first transform the process into a corresponding jump-diffusion with Markovian switching by the supplementary variable technique. Then we prove the Feller and strong Feller properties of the model under some assumptions. Jinying Tong Copyright © 2014 Jinying Tong. All rights reserved. Oscillation Criteria for Functional Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integral Wed, 23 Apr 2014 08:21:23 +0000 http://www.hindawi.com/journals/aaa/2014/697526/ We present new oscillation criteria for the second order nonlinear dynamic equation under mild assumptions. Our results generalize and improve some known results for oscillation of second order nonlinear dynamic equations. Several examples are worked out to illustrate the main results. Yuangong Sun and Taher S. Hassan Copyright © 2014 Yuangong Sun and Taher S. Hassan. All rights reserved. Dynamics of an Information Spreading Model with Isolation Wed, 23 Apr 2014 08:10:13 +0000 http://www.hindawi.com/journals/aaa/2014/484630/ Information plays an important role in modern society. In this paper, we presented a mathematical model of information spreading with isolation. It was found that such a model has rich dynamics including Hopf bifurcation. The results showed that, for a wide range of parameters, there is a bistable phenomenon in the process of information spreading and thus the information cannot be well controlled. Moreover, the model has a limit cycle which implies that the information exhibits periodic outbreak which is consistent with the observations in the real world. Xia-Xia Zhao and Jian-Zhong Wang Copyright © 2014 Xia-Xia Zhao and Jian-Zhong Wang. All rights reserved. Multiple Solutions of Second-Order Damped Impulsive Differential Equations with Mixed Boundary Conditions Wed, 23 Apr 2014 07:00:01 +0000 http://www.hindawi.com/journals/aaa/2014/356745/ We use variational methods to investigate the solutions of damped impulsive differential equations with mixed boundary conditions. The conditions for the multiplicity of solutions are established. The main results are also demonstrated with examples. Jian Liu and Lizhao Yan Copyright © 2014 Jian Liu and Lizhao Yan. All rights reserved. Nonlinear Self-Adjoint Classification of a Burgers-KdV Family of Equations Tue, 22 Apr 2014 14:23:21 +0000 http://www.hindawi.com/journals/aaa/2014/804703/ The concepts of strictly, quasi, weak, and nonlinearly self-adjoint differential equations are revisited. A nonlinear self-adjoint classification of a class of equations with second and third order is carried out. Júlio Cesar Santos Sampaio and Igor Leite Freire Copyright © 2014 Júlio Cesar Santos Sampaio and Igor Leite Freire. All rights reserved. Symplectic Schemes for Linear Stochastic Schrödinger Equations with Variable Coefficients Tue, 22 Apr 2014 14:20:40 +0000 http://www.hindawi.com/journals/aaa/2014/427023/ This paper proposes a kind of symplectic schemes for linear Schrödinger equations with variable coefficients and a stochastic perturbation term by using compact schemes in space. The numerical stability property of the schemes is analyzed. The schemes preserve a discrete charge conservation law. They also follow a discrete energy transforming formula. The numerical experiments verify our analysis. Xiuling Yin and Yanqin Liu Copyright © 2014 Xiuling Yin and Yanqin Liu. All rights reserved. Hölder Continuity of a Parametric Generalized Variational Inequality Tue, 22 Apr 2014 13:12:01 +0000 http://www.hindawi.com/journals/aaa/2014/613716/ By using the classic metric projection method, we obtain sufficient conditions for Hölder continuity of the nonunique solution mapping for a parametric generalized variational inequality with respect to data perturbation. The result is different from the recent ones in the literature and has a strong geometric flavor. Li-na Wang and Xiao-bing Li Copyright © 2014 Li-na Wang and Xiao-bing Li. All rights reserved. Comparison Analysis Based on the Cubic Spline Wavelet and Daubechies Wavelet of Harmonic Balance Method Tue, 22 Apr 2014 13:10:10 +0000 http://www.hindawi.com/journals/aaa/2014/634974/ This paper develops a theoretical analysis of harmonic balance method, based on the cubic spline wavelet and Daubechies wavelet, for steady state analysis of nonlinear circuits under periodic excitation. The properties of the resulting Jacobian matrix for harmonic balance are analyzed. Numerical experiments illustrate the theoretical analysis. Jing Gao Copyright © 2014 Jing Gao. All rights reserved. Finite-Time Stability of Fractional-Order BAM Neural Networks with Distributed Delay Tue, 22 Apr 2014 12:13:14 +0000 http://www.hindawi.com/journals/aaa/2014/634803/ Based on the theory of fractional calculus, the generalized Gronwall inequality and estimates of mittag-Leffer functions, the finite-time stability of Caputo fractional-order BAM neural networks with distributed delay is investigated in this paper. An illustrative example is also given to demonstrate the effectiveness of the obtained result. Yuping Cao and Chuanzhi Bai Copyright © 2014 Yuping Cao and Chuanzhi Bai. All rights reserved. Dimensionality Reduction by Weighted Connections between Neighborhoods Tue, 22 Apr 2014 11:54:19 +0000 http://www.hindawi.com/journals/aaa/2014/928136/ Dimensionality reduction is the transformation of high-dimensional data into a meaningful representation of reduced dimensionality. This paper introduces a dimensionality reduction technique by weighted connections between neighborhoods to improve -Isomap method, attempting to preserve perfectly the relationships between neighborhoods in the process of dimensionality reduction. The validity of the proposal is tested by three typical examples which are widely employed in the algorithms based on manifold. The experimental results show that the local topology nature of dataset is preserved well while transforming dataset in high-dimensional space into a new dataset in low-dimensionality by the proposed method. Fuding Xie, Yutao Fan, and Ming Zhou Copyright © 2014 Fuding Xie et al. All rights reserved. Fractional Integral Inequalities via Hadamard’s Fractional Integral Tue, 22 Apr 2014 11:49:56 +0000 http://www.hindawi.com/journals/aaa/2014/563096/ We establish new fractional integral inequalities, via Hadamard’s fractional integral. Several new integral inequalities are obtained, including a Grüss type Hadamard fractional integral inequality, by using Young and weighted AM-GM inequalities. Many special cases are also discussed. Weerawat Sudsutad, Sotiris K. Ntouyas, and Jessada Tariboon Copyright © 2014 Weerawat Sudsutad et al. All rights reserved. Global Finite-Time Stabilization for a Class of Uncertain High-Order Nonlinear Systems Tue, 22 Apr 2014 11:47:06 +0000 http://www.hindawi.com/journals/aaa/2014/384713/ This paper addresses the problem of global finite-time stabilization by state feedback for a class of high-order nonlinear systems under weaker condition. By using the methods of adding a power integrator, a continuous state feedback controller is successfully constructed to guarantee the global finite-time stability of the resulting closed-loop system. A simulation example is provided to illustrate the effectiveness of the proposed approach. Jian Wang, Jing Xie, and Fangzheng Gao Copyright © 2014 Jian Wang et al. All rights reserved. On Fractional SIRC Model with Salmonella Bacterial Infection Tue, 22 Apr 2014 11:44:33 +0000 http://www.hindawi.com/journals/aaa/2014/136263/ We propose a fractional order SIRC epidemic model to describe the dynamics of Salmonella bacterial infection in animal herds. The infection-free and endemic steady sates, of such model, are asymptotically stable under some conditions. The basic reproduction number is calculated, using next-generation matrix method, in terms of contact rate, recovery rate, and other parameters in the model. The numerical simulations of the fractional order SIRC model are performed by Caputo’s derivative and using unconditionally stable implicit scheme. The obtained results give insight to the modelers and infectious disease specialists. Fathalla A. Rihan, Dumitru Baleanu, S. Lakshmanan, and R. Rakkiyappan Copyright © 2014 Fathalla A. Rihan et al. All rights reserved. Identification of the Point Sources in Some Stochastic Wave Equations Tue, 22 Apr 2014 09:54:05 +0000 http://www.hindawi.com/journals/aaa/2014/219876/ We introduce and study a type of (one-dimensional) wave equations with noisy point sources. We first study the existence and uniqueness problem of the equations. Then, we assume that the locations of point sources are unknown but we can observe the solution at some other location continuously in time. We propose an estimator to identify the point source locations and prove the convergence of our estimator. Yaozhong Hu and Guanglin Rang Copyright © 2014 Yaozhong Hu and Guanglin Rang. All rights reserved. Recent Contributions to Fixed Point Theory and Its Applications Tue, 22 Apr 2014 09:50:51 +0000 http://www.hindawi.com/journals/aaa/2014/329815/ Mohamed A. Khamsi, Hichem Ben-El-Mechaiekh, and Bernd Schroeder Copyright © 2014 Mohamed A. Khamsi et al. All rights reserved. Differential Game for a Class of Warfare Dynamic Systems with Reinforcement Based on Lanchester Equation Tue, 22 Apr 2014 08:03:36 +0000 http://www.hindawi.com/journals/aaa/2014/837431/ This paper concerns the optimal reinforcement game problem between two opposing forces in military conflicts. With some moderate assumptions, we employ Lanchester equation and differential game theory to develop a corresponding optimization game model. After that, we establish the optimum condition for the differential game problem and give an algorithm to obtain the optimal reinforcement strategies. Furthermore, we also discuss the convergence of the algorithm. Finally, a numerical example illustrates the effectiveness of the presented optimal schemes. Our proposed results provide a theoretical guide for both making warfare command decision and assessing military actions. Xiangyong Chen and Jianlong Qiu Copyright © 2014 Xiangyong Chen and Jianlong Qiu. All rights reserved. Convertible Bonds with Higher Loan Rate: Model, Valuation, and Optimal Strategy Tue, 22 Apr 2014 08:03:06 +0000 http://www.hindawi.com/journals/aaa/2014/341519/ We study the pricing problem for convertible bonds via backward stochastic differential equations (BSDEs). By virtue of reflected BSDEs and Malliavin derivatives, we establish the formulae for the fair price of convertible bonds and the hedging portfolio strategy explicitly. We also obtain the optimal conversion time when there is no dividends-paying for underlying common stocks. Furthermore, we consider the case that the loan rate is higher than riskless interest rate in a financial market, and conclude that it does not affect the price of convertible bonds actually. To illustrate our results, some numerical simulations are given and discussed at last. Haiyang Wang and Zhen Wu Copyright © 2014 Haiyang Wang and Zhen Wu. All rights reserved. Chebyshev Type Integral Inequalities Involving the Fractional Hypergeometric Operators Tue, 22 Apr 2014 07:54:33 +0000 http://www.hindawi.com/journals/aaa/2014/609160/ By making use of the fractional hypergeometric operators, we establish certain new fractional integral inequalities for synchronous functions which are related to the weighted version of the Chebyshev functional. Some consequent results and special cases of the main results are also pointed out. D. Baleanu and S. D. Purohit Copyright © 2014 D. Baleanu and S. D. Purohit. All rights reserved. Algorithmic Approach to the Equilibrium Points and Fixed Points Tue, 22 Apr 2014 06:55:29 +0000 http://www.hindawi.com/journals/aaa/2014/468593/ The equilibrium and fixed point problems are considered. An iterative algorithm is presented. Convergence analysis of the algorithm is provided. Lijin Guo, Shin Min Kang, and Young Chel Kwun Copyright © 2014 Lijin Guo et al. All rights reserved. Erratum to “Nonlinear Dynamics in a Cournot Duopoly with Different Attitudes towards Strategic Uncertainty” Tue, 22 Apr 2014 05:59:32 +0000 http://www.hindawi.com/journals/aaa/2014/673427/ Luciano Fanti, Luca Gori, and Mauro Sodini Copyright © 2014 Luciano Fanti et al. All rights reserved. On the Tumura-Clunie Theorem and Its Application Tue, 22 Apr 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/615351/ We cast aside the restriction of the simple pole in the Tumura-Clunie type theorems for meromorphic functions and obtain a better result which improves the earlier results of Y. D. Ren. Furthermore, as an application, we improve a theorem given by B. Y. Su. Gaixian Xue and Jinjin Huang Copyright © 2014 Gaixian Xue and Jinjin Huang. All rights reserved. On Generalized Fractional Integral Operators and the Generalized Gauss Hypergeometric Functions Tue, 22 Apr 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/630840/ A remarkably large number of fractional integral formulas involving the number of special functions, have been investigated by many authors. Very recently, Agarwal (National Academy Science Letters) gave some integral transform and fractional integral formulas involving the . In this sequel, here, we aim to establish some image formulas by applying generalized operators of the fractional integration involving Appell’s function due to Marichev-Saigo-Maeda. Some interesting special cases of our main results are also considered. Dumitru Baleanu and Praveen Agarwal Copyright © 2014 Dumitru Baleanu and Praveen Agarwal. All rights reserved. Impulsive Problems for Fractional Differential Equations with Nonlocal Boundary Value Conditions Tue, 22 Apr 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/510808/ We investigate the nonlocal boundary value problems of impulsive fractional differential equations. By Banach’s contraction mapping principle, Schaefer’s fixed point theorem, and the nonlinear alternative of Leray-Schauder type, some related new existence results are established via a new special hybrid singular type Gronwall inequality. At last, some examples are also given to illustrate the results. Peiluan Li and Youlin Shang Copyright © 2014 Peiluan Li and Youlin Shang. All rights reserved. Nonrigid Registration of Monomodal MRI Using Linear Viscoelastic Model Tue, 22 Apr 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/792194/ This paper describes a method for nonrigid registration of monomodal MRI based on physical laws. The proposed method assumes that the properties of image deformations are like those of viscoelastic matter, which exhibits the properties of both an elastic solid and a viscous fluid. Therefore, the deformation fields of the deformed image are constrained by both sets of properties. After global registration, the local shape variations are assumed to have the properties of the Maxwell model of linear viscoelasticity, and the deformation fields are constrained by the corresponding partial differential equations. To speed up the registration, an adaptive force is introduced according to the maximum displacement of each iteration. Both synthetic datasets and real datasets are used to evaluate the proposed method. We compare the results of the linear viscoelastic model with those of the fluid model on the basis of both the standard and adaptive forces. The results demonstrate that the adaptive force increases in both models and that the linear viscoelastic model improves the registration accuracy. Jian Yang, Yang Chen, Jingfan Fan, and Songyuan Tang Copyright © 2014 Jian Yang et al. All rights reserved. Almost Periodic Solution of a Modified Leslie-Gower Predator-Prey Model with Beddington-DeAngelis Functional Response and Feedback Controls Tue, 22 Apr 2014 00:00:00 +0000 http://www.hindawi.com/journals/aaa/2014/252579/ We consider a modified Leslie-Gower predator-prey model with the Beddington-DeAngelis functional response and feedback controls as follows: , , , and . Sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained. Kerong Zhang, Jianli Li, and Aiwen Yu Copyright © 2014 Kerong Zhang et al. All rights reserved.