## Abstract and Applied Analysis

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

### 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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