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International Journal of Differential Equations
Volume 2011 (2011), Article ID 814132, 8 pages
http://dx.doi.org/10.1155/2011/814132
Research Article

New Method for Solving Linear Fractional Differential Equations

Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt

Received 4 May 2011; Revised 21 July 2011; Accepted 25 July 2011

Academic Editor: Shaher M. Momani

Copyright © 2011 S. Z. Rida and A. A. M. Arafa. 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 develop a new application of the Mittag-Leffler Function method that will extend the application of the method to linear differential equations with fractional order. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided. The results reveal that the technique introduced here is very effective and convenient for solving linear differential equations of fractional order.