A fractional-order Jacobi Tau method for a class of time-fractional PDEs with variable coefficients

This paper presents a shifted fractional-order Jacobi orthogonal function (SFJF) based on the definition of the classical Jacobi polynomial. A new fractional integral operational matrix of the SFJF is presented and derived. We propose the spectral Tau method, in conjunction with the operational matrices of the Riemann-Liouville fractional integral for SFJF and derivative for Jacobi polynomial, to solve a class of time-fractional partial differential equations with variable coefficients. In this algorithm, the approximate solution is expanded by means of both SFJFs for temporal discretization and Jacobi polynomials for spatial discretization. The proposed tau scheme, both in temporal and spatial discretizations, successfully reduced such problem into a system of algebraic equations, which is far easier to be solved. Numerical results are provided to demonstrate the high accuracy and superiority of the proposed algorithm over existing ones. Copyright (C) 2015 John Wiley & Sons, Ltd.