Abstract and Applied Analysis
Volume 2012 (2012), Article ID 426514, 9 pages
http://dx.doi.org/10.1155/2012/426514
Research Article

Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions

Adel Al-Rabtah,1 Shaher Momani,2 and Mohamed A. Ramadan3

1Department of Mathematics and Statistics, Mutah University, P.O. Box 7, Al-Karak, Jordan
2Department of Mathematics and Statistics, University of Jordan, Amman 11942, Jordan
3Department of Mathematics, Faculty of Science, Minoufiya University, Shebeen El Koom, Minoufiya, Egypt

Received 29 November 2011; Revised 23 December 2011; Accepted 26 December 2011

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 Adel Al-Rabtah 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

Suitable spline functions of polynomial form are derived and used to solve linear and nonlinear fractional differential equations. The proposed method is applicable for 0<α≤1 and α≥1, where α denotes the order of the fractional derivative in the Caputo sense. The results obtained are in good agreement with the exact analytical solutions and the numerical results presented elsewhere. Results also show that the technique introduced here is robust and easy to apply.