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A quadrature tau method for fractional differential equations with variable coefficients. (English) Zbl 1269.65068
Summary: We develop a direct solution technique for solving multi-order fractional differential equations (FDEs) with variable coefficients using a quadrature shifted Legendre tau (Q-SLT) method. The spatial approximation is based on shifted Legendre polynomials. A new formula expressing explicitly any fractional-order derivatives of shifted Legendre polynomials of any degree in terms of shifted Legendre polynomials themselves is proved. Extension of the tau method for FDEs with variable coefficients is treated using the shifted Legendre-Gauss-Lobatto quadrature. Numerical results are given to confirm the reliability of the proposed method for some FDEs with variable coefficients.
65L05Initial value problems for ODE (numerical methods)
34A08Fractional differential equations
34A30Linear ODE and systems, general
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