The operational matrix of fractional integration for shifted Chebyshev polynomials. (English) Zbl 1255.65147

Bhrawy, A. H.; Alofi, A. S.

Appl. Math. Lett. 26, No. 1, 25-31 (2013).

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:

65L60	Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
65L05	Numerical methods for initial value problems involving ordinary differential equations
34A30	Linear ordinary differential equations and systems

Keywords:

operational matrix; shifted Chebyshev polynomials; tau method; multi-term FDEs; numerical examples; spectral method; linear fractinal differential equation