Abstract and Applied Analysis

An Efficient Series Solution for Fractional Differential Equations

Mohammed Al-Refai, Mohamed Ali Hajji, and Muhammad I. Syam

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 891837, 7 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412607143

Digital Object Identifier
doi:10.1155/2014/891837

Mathematical Reviews number (MathSciNet)
MR3198267

Zentralblatt MATH identifier
07023252

Citation

Al-Refai, Mohammed; Ali Hajji, Mohamed; Syam, Muhammad I. An Efficient Series Solution for Fractional Differential Equations. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 891837, 7 pages. doi:10.1155/2014/891837. https://projecteuclid.org/euclid.aaa/1412607143


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