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A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order. (English) Zbl 1231.65126
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.

65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
34A08Fractional differential equations
45J05Integro-ordinary differential equations
Full Text: DOI
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