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The operational matrix of fractional integration for shifted Chebyshev polynomials. (English) Zbl 1255.65147
Summary: A new shifted Chebyshev operational matrix of fractional integration of arbitrary order is introduced and applied together with the spectral tau method for solving linear fractional differential equations (FDEs). The fractional integration is described in the Riemann-Liouville sense. The numerical approach is based on the shifted Chebyshev tau method. The main characteristic behind the approach using this technique is that only a small number of shifted Chebyshev polynomials is needed to obtain a satisfactory result. Illustrative examples reveal that the present method is very effective and convenient for linear multi-term FDEs.
MSC:
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
65L05Initial value problems for ODE (numerical methods)
34A30Linear ODE and systems, general