International Journal of Mathematics and Mathematical Sciences
Volume 2012 (2012), Article ID 638026, 16 pages
http://dx.doi.org/10.1155/2012/638026
Research Article

The Use of Cubic Splines in the Numerical Solution of Fractional Differential Equations

W. K. Zahra1 and S. M. Elkholy2

1Department of Physics and Engineering Mathematics, Faculty of Engineering, Tanta University, 31521 Tanta, Egypt
2Department of Engineering Physics and Mathematics, Faculty of Engineering, Kafr El Sheikh University, Kafr El Sheikh, Egypt

Received 31 March 2012; Revised 8 May 2012; Accepted 23 May 2012

Academic Editor: Manfred Moller

Copyright © 2012 W. K. Zahra and S. M. Elkholy. 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

Fractional calculus became a vital tool in describing many phenomena appeared in physics, chemistry as well as engineering fields. Analytical solution of many applications, where the fractional differential equations appear, cannot be established. Therefore, cubic polynomial spline-function-based method combined with shooting method is considered to find approximate solution for a class of fractional boundary value problems (FBVPs). Convergence analysis of the method is considered. Some illustrative examples are presented.