Spectral collocation method for linear fractional integro-differential equations

In this paper, we propose and analyze a spectral Jacobi-collocation method for the numerical solution of general linear fractional integro-differential equations. The fractional derivatives are described in the Caputo sense. First, we use some function and variable transformations to change the equation into a Volterra integral equation defined on the standard interval [-1,1][-1,1]. Then the Jacobi–Gauss points are used as collocation nodes and the Jacobi–Gauss quadrature formula is used to approximate the integral equation. Later, the convergence order of the proposed method is investigated in the infinity norm. Finally, some numerical results are given to demonstrate the effectiveness of the proposed method.