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 Table of Contents
Advanced Theoretical and Applied Studies of Fractional Differential Equations
“Advanced Theoretical and Applied Studies of Fractional Differential Equations” is an annual special issue published in “Abstract and Applied Analysis.” The current issue is the 2013 issue, which is now closed for submissions.
Advanced Theoretical and Applied Studies of Fractional Differential Equations 2013
Guest Editors:
Dumitru Baleanu, Juan J. Trujillo, and Bashir Ahmad

Asymptotic Behavior of Solutions to Abstract Stochastic Fractional Partial Integrodifferential Equations, ZhiHan Zhao, YongKui Chang, and Juan J. Nieto
Volume 2013 (2013), Article ID 138068, 8 pages 
Fractional Cauchy Problem with RiemannLiouville Derivative on Time Scales, Ling Wu and Jiang Zhu
Volume 2013 (2013), Article ID 795701, 23 pages 
Global Solvability of Hammerstein Equations with Applications to BVP Involving Fractional Laplacian, Dorota Bors
Volume 2013 (2013), Article ID 240863, 10 pages 
Amplitude Modulation and Synchronization of FractionalOrder MemristorBased Chua's Circuit, A. G. Radwan, K. Moaddy, and I. Hashim
Volume 2013 (2013), Article ID 758676, 10 pages 
On a Fractional Nonlinear Hyperbolic Equation Arising from Relative Theory, Zujin Zhang, Xiaofeng Wang, and Zhengan Yao
Volume 2013 (2013), Article ID 548562, 6 pages 
Sliding Mode Control of the FractionalOrder Unified Chaotic System, Jian Yuan, Bao Shi, Xiaoyun Zeng, Wenqiang Ji, and Tetie Pan
Volume 2013 (2013), Article ID 397504, 13 pages 
Estimates of Some Operators on OneSided Weighted Morrey Spaces, Shaoguang Shi and Zunwei Fu
Volume 2013 (2013), Article ID 829218, 9 pages 
The Existence of Positive Solutions for a New Coupled System of Multiterm Singular Fractional Integrodifferential Boundary Value Problems, Dumitru Baleanu, Sayyedeh Zahra Nazemi, and Shahram Rezapour
Volume 2013 (2013), Article ID 368659, 15 pages 
A New Numerical Algorithm for Solving a Class of Fractional AdvectionDispersion Equation with Variable Coefficients Using Jacobi Polynomials, A. H. Bhrawy
Volume 2013 (2013), Article ID 954983, 9 pages 
Application of the Local Fractional Series Expansion Method and the Variational Iteration Method to the Helmholtz Equation Involving Local Fractional Derivative Operators, AiMin Yang, ZengShun Chen, H. M. Srivastava, and XiaoJun Yang
Volume 2013 (2013), Article ID 259125, 6 pages 
Existence for Nonautonomous Fractional Integrodifferential Equations with Nonlocal Conditions, Fang Li
Volume 2013 (2013), Article ID 723453, 8 pages 
Modeling a Microstretch Thermoelastic Body with Two Temperatures, M. Marin, R. P. Agarwal, and S. R. Mahmoud
Volume 2013 (2013), Article ID 583464, 7 pages 
Positive Solutions of Nonlocal Boundary Value Problem for HighOrder Nonlinear Fractional Difference Equations, Changlong Yu and Jufang Wang
Volume 2013 (2013), Article ID 928147, 9 pages 
Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces, Mourad Kerboua, Amar Debbouche, and Dumitru Baleanu
Volume 2013 (2013), Article ID 262191, 10 pages 
Fractional Partial Differential Equation: Fractional Total Variation and Fractional Steepest Descent ApproachBased Multiscale Denoising Model for Texture Image, YiFei Pu, JiLiu Zhou, Patrick Siarry, Ni Zhang, and YiGuang Liu
Volume 2013 (2013), Article ID 483791, 19 pages 
Existence Theory for th Order Nonlocal Integral Boundary Value Problems and Extension to Fractional Case, Bashir Ahmad, Sotiris K. Ntouyas, and Hamed H. Alsulami
Volume 2013 (2013), Article ID 183813, 12 pages 
Explicit Solutions of Singular Differential Equation by Means of Fractional Calculus Operators, Resat Yilmazer and Okkes Ozturk
Volume 2013 (2013), Article ID 715258, 6 pages 
A Study of Nonlinear Fractional Difference Equations with Nonlocal Integral Boundary Conditions, Ahmed Alsaedi, Bashir Ahmad, and Hana AlHutami
Volume 2013 (2013), Article ID 410505, 8 pages 
A Spectral Deferred Correction Method for Fractional Differential Equations, Jia Xin, Jianfei Huang, Weijia Zhao, and Jiang Zhu
Volume 2013 (2013), Article ID 139530, 6 pages 
The Existence of Positive Solutions for Boundary Value Problem of the Fractional SturmLiouville Functional Differential Equation, Yanan Li, Shurong Sun, Zhenlai Han, and Hongling Lu
Volume 2013 (2013), Article ID 301560, 20 pages 
Solutions of Fractional KonopelchenkoDubrovsky and NizhnikNovikovVeselov Equations Using a Generalized Fractional Subequation Method, Yanqin Liu and Limei Yan
Volume 2013 (2013), Article ID 839613, 7 pages 
The Modified Trial Equation Method for Fractional Wave Equation and Time Fractional Generalized Burgers Equation, Hasan Bulut, Haci Mehmet Baskonus, and Yusuf Pandir
Volume 2013 (2013), Article ID 636802, 8 pages 
Lower and Upper Solutions Method for Positive Solutions of Fractional Boundary Value Problems, R. Darzi, B. Mohammadzadeh, A. Neamaty, and D. Bǎleanu
Volume 2013 (2013), Article ID 847184, 7 pages 
A New Legendre Spectral Galerkin and PseudoSpectral Approximations for Fractional Initial Value Problems, A. H. Bhrawy and M. A. Alghamdi
Volume 2013 (2013), Article ID 306746, 10 pages 
Revised Variational Iteration Method for Solving Systems of Nonlinear FractionalOrder Differential Equations, C. Ünlü, H. Jafari, and D. Baleanu
Volume 2013 (2013), Article ID 461837, 7 pages 
Numerical Algorithms for the Fractional DiffusionWave Equation with Reaction Term, Hengfei Ding and Changpin Li
Volume 2013 (2013), Article ID 493406, 15 pages 
An Interior Inverse Problem for the Diffusion Operator, A. Dabbaghian, H. Jafari, and N. Yosofi
Volume 2013 (2013), Article ID 320456, 6 pages 
Nonlocal Integrodifferential Boundary Value Problem for Nonlinear Fractional Differential Equations on an Unbounded Domain, Lihong Zhang, Bashir Ahmad, Guotao Wang, Ravi P. Agarwal, Maryem AlYami, and Wafa Shammakh
Volume 2013 (2013), Article ID 813903, 5 pages 
Positive Solutions to Fractional Boundary Value Problems with Nonlinear Boundary Conditions, Nemat Nyamoradi, Dumitru Baleanu, and Tahereh Bashiri
Volume 2013 (2013), Article ID 579740, 20 pages 
Root Locus Practical Sketching Rules for FractionalOrder Systems, António M. Lopes and J. A. Tenreiro Machado
Volume 2013 (2013), Article ID 102068, 14 pages 
Stability and Convergence of a TimeFractional Variable Order Hantush Equation for a Deformable Aquifer, Abdon Atangana and S. C. Oukouomi Noutchie
Volume 2013 (2013), Article ID 691060, 8 pages 
Fractional Coins and Fractional Derivatives, J. A. Tenreiro Machado
Volume 2013 (2013), Article ID 205097, 5 pages 
Advanced Theoretical and Applied Studies of Fractional Differential Equations 2013, Dumitru Baleanu, Juan J. Trujillo, and Bashir Ahmad
Volume 2014 (2014), Article ID 896105, 1 page 
Convoluted Fractional Semigroups and Fractional Abstract Cauchy Problems, ZhanDong Mei, JiGen Peng, and JingHuai Gao
Volume 2014 (2014), Article ID 357821, 9 pages
Advanced Theoretical and Applied Studies of Fractional Differential Equations 2012
Guest Editors: Dumitru Baleanu, Juan J. Trujillo, and Bashir Ahmad

Fractional Difference Equations with Real Variable, JinFa Cheng and YuMing Chu
Volume 2012 (2012), Article ID 918529, 24 pages 
An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems, Mohammad Maleki, Ishak Hashim, Majid Tavassoli Kajani, and Saeid Abbasbandy
Volume 2012 (2012), Article ID 381708, 19 pages 
Numerical Solutions to Fractional Perturbed Volterra Equations, B. Bandrowski, A. Karczewska, and P. Rozmej
Volume 2012 (2012), Article ID 529602, 19 pages 
Robust Position Control of PMSM Using FractionalOrder Sliding Mode Controller, Jiacai Huang, Hongsheng Li, YangQuan Chen, and Qinghong Xu
Volume 2012 (2012), Article ID 512703, 33 pages 
On a Class of Abstract TimeFractional Equations on Locally Convex Spaces, Marko Kostić, ChengGang Li, and Miao Li
Volume 2012 (2012), Article ID 131652, 41 pages 
Existence of Mild Solutions for a Class of Fractional Evolution Equations with Compact Analytic Semigroup, He Yang
Volume 2012 (2012), Article ID 903518, 15 pages 
A Characteristic Difference Scheme for TimeFractional Heat Equations Based on the CrankNicholson Difference Schemes, Ibrahim Karatay and Serife R. Bayramoglu
Volume 2012 (2012), Article ID 548292, 11 pages 
Alternative Forms of Compound Fractional Poisson Processes, Luisa Beghin and Claudio Macci
Volume 2012 (2012), Article ID 747503, 30 pages 
Dynamic Properties of a Forest Fire Model, Na Min, Hongyang Zhang, and Zhilin Qu
Volume 2012 (2012), Article ID 948480, 13 pages 
On the Definitions of Nabla Fractional Operators, Thabet Abdeljawad and Ferhan M. Atici
Volume 2012 (2012), Article ID 406757, 13 pages 
Application of Homotopy Perturbation and Variational Iteration Methods for Fredholm Integrodifferential Equation of Fractional Order, Asma Ali Elbeleze, Adem Kiliçman, and Bachok M. Taib
Volume 2012 (2012), Article ID 763139, 14 pages 
Shannon Information and Power Law Analysis of the Chromosome Code, J. A. Tenreiro Machado
Volume 2012 (2012), Article ID 439089, 13 pages 
ObserverType Consensus Protocol for a Class of FractionalOrder Uncertain Multiagent Systems, Hongjie Li
Volume 2012 (2012), Article ID 672346, 18 pages 
Positive Solutions for Nonlinear Fractional Differential Equations with Boundary Conditions Involving RiemannStieltjes Integrals, Jiqiang Jiang, Lishan Liu, and Yonghong Wu
Volume 2012 (2012), Article ID 708192, 21 pages 
A Weighted Variant of RiemannLiouville Fractional Integrals on , Zun Wei Fu, Shan Zhen Lu, and Wen Yuan
Volume 2012 (2012), Article ID 780132, 18 pages 
Existence of Three Solutions for a Nonlinear Fractional Boundary
Value Problem via a Critical Points Theorem, Chuanzhi Bai
Volume 2012 (2012), Article ID 963105, 13 pages 
Finite Element Solutions for the Space Fractional Diffusion Equation with a Nonlinear Source Term, Y. J. Choi and S. K. Chung
Volume 2012 (2012), Article ID 596184, 25 pages 
Dynamic Properties of the FractionalOrder Logistic Equation of Complex Variables, A. M. A. ElSayed, E. Ahmed, and H. A. A. ElSaka
Volume 2012 (2012), Article ID 251715, 12 pages 
A Note on Impulsive Fractional Evolution Equations with Nondense Domain, Zufeng Zhang and Bin Liu
Volume 2012 (2012), Article ID 359452, 13 pages 
Existence and Uniqueness of Positive Solutions for a Singular Fractional ThreePoint Boundary Value Problem, I. J. Cabrera, J. Harjani, and K. B. Sadarangani
Volume 2012 (2012), Article ID 803417, 18 pages 
On Antiperiodic Boundary Value Problems for HigherOrder Fractional Differential Equations, Ahmed Alsaedi, Bashir Ahmad, and Afrah Assolami
Volume 2012 (2012), Article ID 325984, 15 pages 
Positive Solutions for a Fractional Boundary Value Problem with Changing Sign Nonlinearity, Yongqing Wang, Lishan Liu, and Yonghong Wu
Volume 2012 (2012), Article ID 214042, 17 pages 
Coupled Coincidence Point and Coupled Fixed Point Theorems via Generalized MeirKeeler Type Contractions, Hassen Aydi, Erdal Karapınar, and İnci M. Erhan
Volume 2012 (2012), Article ID 781563, 22 pages 
The Existence of Positive Solutions for Fractional Differential Equations with Sign Changing Nonlinearities, Weihua Jiang, Jiqing Qiu, and Weiwei Guo
Volume 2012 (2012), Article ID 180672, 13 pages 
Existence and Uniqueness of Solutions for Initial Value Problem of Nonlinear Fractional Differential Equations, Qiuping Li, Shurong Sun, Ping Zhao, and Zhenlai Han
Volume 2012 (2012), Article ID 615230, 14 pages 
Advanced Theoretical and Applied Studies of Fractional Differential Equations, Dumitru Baleanu, Juan J. Trujillo, and Bashir Ahmad
Volume 2013 (2013), Article ID 195429, 1 page 
A New Fractional Integral Inequality with Singularity and Its Application, QiongXiang Kong and XiaoLi Ding
Volume 2012 (2012), Article ID 937908, 12 pages 
A Multidimensional Scaling Analysis of Musical Sounds Based on Pseudo Phase Plane, Miguel F. M. Lima, J. A. Tenreiro Machado, and António C. Costa
Volume 2012 (2012), Article ID 436108, 14 pages 
Existence and Uniqueness of Solution for a Class of Nonlinear Fractional Order Differential Equations, Azizollah Babakhani and Dumitru Baleanu
Volume 2012 (2012), Article ID 632681, 14 pages 
Positive Solutions of an Initial Value Problem for Nonlinear Fractional Differential Equations, D. Baleanu, H. Mohammadi, and Sh. Rezapour
Volume 2012 (2012), Article ID 837437, 7 pages 
A Coupled System of Nonlinear Fractional Differential Equations with Multipoint Fractional Boundary Conditions on an Unbounded Domain, Guotao Wang, Bashir Ahmad, and Lihong Zhang
Volume 2012 (2012), Article ID 248709, 11 pages 
On a Differential Equation Involving HilferHadamard Fractional Derivative, M. D. Qassim, K. M. Furati, and N.E. Tatar
Volume 2012 (2012), Article ID 391062, 17 pages 
The Approximate Solution of Fractional Fredholm Integrodifferential Equations by Variational Iteration and Homotopy Perturbation Methods, Abdelouahab Kadem and Adem Kilicman
Volume 2012 (2012), Article ID 486193, 10 pages 
A Generalized qMittagLeffler Function by qCaptuo Fractional Linear Equations, Thabet Abdeljawad, BetÃ¼l Benli, and Dumitru Baleanu
Volume 2012 (2012), Article ID 546062, 11 pages 
The Positive Properties of Green’s Function for Fractional Differential Equations and Its Applications, Fuquan Jiang, Xiaojie Xu, and Zhongwei Cao
Volume 2013 (2013), Article ID 531038, 12 pages 
On the Laws of Total Local Times for Paths and Bridges of Symmetric Lévy Processes, Masafumi Hayashi and Kouji Yano
Volume 2013 (2013), Article ID 463857, 12 pages