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http://dx.doi.org/10.14317/jami.2013.299

FRACTIONAL CHEBYSHEV FINITE DIFFERENCE METHOD FOR SOLVING THE FRACTIONAL BVPS  

Khader, M.M. (Department of Mathematics, Faculty of Sceince, Benha University)
Hendy, A.S. (Department of Mathematics, Faculty of Sceince, Benha University)
Publication Information
Journal of applied mathematics & informatics / v.31, no.1_2, 2013 , pp. 299-309 More about this Journal
Abstract
In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method (FChFD). The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. We tested this technique to solve numerically fractional BVPs. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The fractional derivatives are presented in terms of Caputo sense. The application of the method to fractional BVPs leads to algebraic systems which can be solved by an appropriate method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.
Keywords
Fractional Chebyshev approximations; Fractional BVPs; Finite difference method; Caputo fractional derivatives; Operational matrix method; Gauss-Lobatto nodes;
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