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Journal of Applied Mathematics
Volume 2012, Article ID 542401, 19 pages
http://dx.doi.org/10.1155/2012/542401
Research Article

Wavelet Collocation Method for Solving Multiorder Fractional Differential Equations

Faculty of Mathematics, Yazd University, Yazd, Iran

Received 15 July 2011; Accepted 27 October 2011

Academic Editor: Md. Sazzad Chowdhury

Copyright © 2012 M. H. Heydari 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

The operational matrices of fractional-order integration for the Legendre and Chebyshev wavelets are derived. Block pulse functions and collocation method are employed to derive a general procedure for forming these matrices for both the Legendre and the Chebyshev wavelets. Then numerical methods based on wavelet expansion and these operational matrices are proposed. In this proposed method, by a change of variables, the multiorder fractional differential equations (MOFDEs) with nonhomogeneous initial conditions are transformed to the MOFDEs with homogeneous initial conditions to obtain suitable numerical solution of these problems. Numerical examples are provided to demonstrate the applicability and simplicity of the numerical scheme based on the Legendre and Chebyshev wavelets.