This paper deals with the stability of nonlinear fractional differential systems equipped with the Caputo derivative. At first, a sufficient condition on asymptotical stability is established by using a Lyapunov-like function. Then, the fractional differential inequalities and comparison method are applied to the analysis of the stability of fractional differential systems. In addition, some ot...

In this paper, we investigate the numerical solution of fractional integro-differential equations by comparison between He’s variational iteration method and taylor expansion method. The fractional derivative is described in the Caputo sense. Some numerical examples are presented to illustrate the methods.

In this paper, the Homotopy perturbation method is successfully extended to solve fractional biological population model and numerical results are obtained. The fractional derivatives are described in the Caputo sense, some examples are provided. And the solutions of the equation are continuous with the parameter α . Mathematics subject classification (2010): 35D99.

To obtain the solution of nonlinear sequential fractional differential equations for Caputo operator two methods namely the Adomian decomposition method and DaftardarGejji and Jafari iterative method are applied in this paper. Finally some examples are presented to illustrate the efficiency of these methods. 2010 Mathematics Subject Classification: 65L05, 26A33

In this paper, a modification of variational iteration method is applied to solve fractional integro-differential equations. The fractional derivative is considered in the Caputo sense. Through examples, we will see the modified method performs extremely effective in terms of efficiency and simplicity to solve fractional integro-differential equations. 2000 Mathematics Subject Classification: 6...

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In this paper we use the upper and lower solutions method to investigate the existence of solutions of a class of impulsive partial hyperbolic differential inclusions at fixed moments of impulse involving the Caputo fractional derivative. These results are obtained upon suitable fixed point theorems.

In this paper we present approximate analytical solution of a time-fractional Zakharov-Kuznetsov equation via the fractional iteration method. The fractional derivatives are described in the Caputo sense. The approximate results show that the fractional iteration method is a very efficient technique to handle fractional partial differential equations.

This paper is devoted to study the existence of solutions for a class of initial value problems for impulsive fractional differential equations involving the Caputo fractional derivative in a Banach space. The arguments are based upon Mönch’s fixed point theorem and the technique of measures of noncompactness.

We consider infinite horizon fractional variational problems, where the fractional derivative is defined in the sense of Caputo. Necessary optimality conditions for higher-order variational problems and optimal control problems are obtained. Transversality conditions are obtained in the case state functions are free at the initial time.