A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order

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Date

2011

Journal Title

Journal ISSN

Volume Title

Type

Article

Publisher

PERGAMON-ELSEVIER SCIENCE LTD

Series Info

COMPUTERS & MATHEMATICS WITH APPLICATIONS;Volume: 62 Issue: 5 Pages: 2364-2373

Scientific Journal Rankings

Abstract

We are concerned with linear and nonlinear multi-term fractional differential equations (FDEs). The shifted Chebyshev operational matrix (COM) of fractional derivatives is derived and used together with spectral methods for solving FDEs. Our approach was based on the shifted Chebyshev tau and collocation methods. The proposed algorithms are applied to solve two types of FDEs, linear and nonlinear, subject to initial or boundary conditions, and the exact solutions are obtained for some tested problems. Numerical results with comparisons are given to confirm the reliability of the proposed method for some FDEs. (C) 2011 Elsevier Ltd. All rights reserved.

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Keywords

October University for Fractional differential equations, Spectral method, Shifted Chebyshev polynomials, Operational matrix, Caputo derivative

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