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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 916456, 15 pages
http://dx.doi.org/10.1155/2013/916456
Research Article

Chebyshev Wavelet Finite Difference Method: A New Approach for Solving Initial and Boundary Value Problems of Fractional Order

1Department of Mathematics, University Putra Malaysia (UPM), 43400 Serdang, Selangor, Malaysia
2Department of Mathematics, Imam Khomeini International University, Ghazvin 34149, Iran

Received 25 April 2013; Revised 30 August 2013; Accepted 9 September 2013

Academic Editor: Andrew Pickering

Copyright © 2013 A. Kazemi Nasab 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

A new method based on a hybrid of Chebyshev wavelets and finite difference methods is introduced for solving linear and nonlinear fractional differential equations. The useful properties of the Chebyshev wavelets and finite difference method are utilized to reduce the computation of the problem to a set of linear or nonlinear algebraic equations. This method can be considered as a nonuniform finite difference method. Some examples are given to verify and illustrate the efficiency and simplicity of the proposed method.