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

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 colloc...

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Bibliographic Details
Published inComputers & mathematics with applications (1987) Vol. 62; no. 5; pp. 2364 - 2373
Main Authors Doha, E.H., Bhrawy, A.H., Ezz-Eldien, S.S.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.09.2011
Subjects
Caputo derivative
Chebyshev approximation
Derivatives
Differential equations
Exact solutions
Fractional differential equations
Mathematical analysis
Mathematical models
Nonlinearity
Operational matrix
Shifted Chebyshev polynomials
Spectral method
Spectral methods
Operational matrix
Spectral method
Fractional differential equations
Caputo derivative
Shifted Chebyshev polynomials
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Summary: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.
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ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2011.07.024