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Abstract and Applied Analysis
Volume 2014, Article ID 891837, 7 pages
http://dx.doi.org/10.1155/2014/891837
Research Article

An Efficient Series Solution for Fractional Differential Equations

Department of Mathematical Sciences, United Arab Emirates University, P.O. Box 15551, Al Ain, UAE

Received 25 January 2014; Revised 18 February 2014; Accepted 24 March 2014; Published 6 April 2014

Academic Editor: Dumitru Baleanu

Copyright © 2014 Mohammed Al-Refai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce a simple and efficient series solution for a class of nonlinear fractional differential equations of Caputo's type. The new approach is a modified form of the well-known Taylor series expansion where we overcome the difficulty of computing iterated fractional derivatives, which do not compute in general. The terms of the series are determined sequentially with explicit formula, where only integer derivatives have to be computed. The efficiency of the new algorithm is illustrated through several examples. Comparison with other series methods such as the Adomian decomposition method and the homotopy perturbation method is made to indicate the efficiency of the new approach. The algorithm can be implemented for a wide class of fractional differential equations with different types of fractional derivatives.