Advanced Theoretical and Applied Studies of Fractional Differential Equations 2013 by Dumitru Baleanu, Juan J. Trujillo, Bashir Ahmad

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Controllability of Mild Solution of Nonlocal Conformable Fractional Differential Equations by Mohamed Hannabou, Mohamed Bouaouid, Khalid Hilal

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Oscillation of a Class of Fractional Differential Equations with Damping Term by Huizeng Qin, Bin Zheng

“…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. …”
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Recent Advance in Function Spaces and Their Applications in Fractional Differential Equations by Xinguang Zhang, Lishan Liu, Yonghong Wu, Liguang Wang

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Existence of Positive Solution for BVP of Nonlinear Fractional Differential Equation by Jun-Rui Yue, Jian-Ping Sun, Shuqin Zhang

“…We consider the following boundary value problem of nonlinear fractional differential equation: (CD0+αu)(t)=f(t,u(t)),  t∈[0,1],  u(0)=0,   u′(0)+u′′(0)=0,  u′(1)+u′′(1)=0, where α∈(2,3] is a real number,  CD0+α denotes the standard Caputo fractional derivative, and f:[0,1]×[0,+∞)→[0,+∞) is continuous. …”
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The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations by W. K. Zahra, S. M. Elkholy

“…Analytical solution of many applications, where the fractional differential equations appear, cannot be established. …”
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Modified Homotopy Perturbation Method for Solving Fractional Differential Equations by A. A. Hemeda

“…This work will present a numerical comparison between the considered method and some other methods through solving various fractional differential equations in applied fields. The obtained results reveal that this method is very effective and simple, accelerates the rapid convergence of the series solution, and reduces the size of work to only one iteration.…”
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Asymptotically Linear Solutions for Some Linear Fractional Differential Equations by Dumitru Baleanu, Octavian G. Mustafa, Ravi P. Agarwal

“…We establish here that under some simple restrictions on the functional coefficient a(t) the fractional differential equation D0tα[tx′−x+x(0)]+a(t)x=0,  t>0, has a solution expressible as ct+d+o(1) for t→+∞, where D0tα designates the Riemann-Liouville derivative of order α∈(0,1) and c,d∈ℝ.…”
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Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation by Moustafa El-Shahed

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Three-Point Boundary Value Problems for Conformable Fractional Differential Equations by H. Batarfi, Jorge Losada, Juan J. Nieto, W. Shammakh

“…We study a fractional differential equation using a recent novel concept of fractional derivative with initial and three-point boundary conditions. …”
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Eigenvalue Problem for Nonlinear Fractional Differential Equations with Integral Boundary Conditions by Guotao Wang, Sanyang Liu, Lihong Zhang

“…By employing known Guo-Krasnoselskii fixed point theorem, we investigate the eigenvalue interval for the existence and nonexistence of at least one positive solution of nonlinear fractional differential equation with integral boundary conditions.…”
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Improvement on Conformable Fractional Derivative and Its Applications in Fractional Differential Equations by Feng Gao, Chunmei Chi

“…We also gave the definition of the corresponding fractional integral and illustrated the applications of the improved conformable derivative to fractional differential equations by some examples.…”
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Analytical Solutions of Fractional Differential Equations Using the Convenient Adomian Series by Xiang-Chao Shi, Lan-Lan Huang, Zhen-Guo Deng, Dan Liu

“…In this paper, the Adomian decomposition method is applied to nonlinear fractional differential equation and the error analysis is given which shows the convenience.…”
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Positive Solutions for BVP of Fractional Differential Equation with Integral Boundary Conditions by Min Li, Jian-Ping Sun, Ya-Hong Zhao

“…In this paper, we consider a class of boundary value problems of nonlinear fractional differential equation with integral boundary conditions. …”
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Iterative Construction of Fixed Points for Functional Equations and Fractional Differential Equations by Latif Ur Rahman, Muhammad Arshad, Sabri T. M. Thabet, Imed Kedim

“…This paper proposes some iterative constructions of fixed points for showing the existence and uniqueness of solutions for functional equations and fractional differential equations (FDEs) in the framework of CAT (0) spaces. …”
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Solution of Sequential Hadamard Fractional Differential Equations by Variation of Parameter Technique by Mohammed M. Matar

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Solvability and Optimal Controls of Semilinear Riemann-Liouville Fractional Differential Equations by Xue Pan, Xiuwen Li, Jing Zhao

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Existence of Solutions of Fractional Differential Equation with p-Laplacian Operator at Resonance by Zhigang Hu, Wenbin Liu, Jiaying Liu

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On Coupled p-Laplacian Fractional Differential Equations with Nonlinear Boundary Conditions by Aziz Khan, Yongjin Li, Kamal Shah, Tahir Saeed Khan

“…This paper is related to the existence and uniqueness of solutions to a coupled system of fractional differential equations (FDEs) with nonlinear p-Laplacian operator by using fractional integral boundary conditions with nonlinear term and also to checking the Hyers-Ulam stability for the proposed problem. …”
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Henry-Gronwall Integral Inequalities with “Maxima” and Their Applications to Fractional Differential Equations by Phollakrit Thiramanus, Jessada Tariboon, Sotiris K. Ntouyas

“…Applications to Caputo fractional differential equations with “maxima” are also presented.…”
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