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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 5234151, 10 pages
https://doi.org/10.1155/2017/5234151
Research Article

An Efficient Series Solution for Nonlinear Multiterm Fractional Differential Equations

Department of Mathematical Sciences, United Arab Emirates University, Al-Ain, UAE

Correspondence should be addressed to Mohammed Al-Refai; ea.ca.ueau@iaferla_m

Received 24 January 2017; Accepted 21 February 2017; Published 8 March 2017

Academic Editor: Thabet Abdeljawad

Copyright © 2017 Moh’d Khier Al-Srihin and Mohammed Al-Refai. 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

In this paper, we introduce an efficient series solution for a class of nonlinear multiterm fractional differential equations of Caputo type. The approach is a generalization to our recent work for single fractional differential equations. We extend the idea of the Taylor series expansion method to multiterm fractional differential equations, where we overcome the difficulty of computing iterated fractional derivatives, which are difficult to be computed in general. The terms of the series are obtained sequentially using a closed formula, where only integer derivatives have to be computed. Several examples are presented to illustrate the efficiency of the new approach and comparison with the Adomian decomposition method is performed.