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