Abstract The aim of this paper is to propose an efficient spectral-Galerkin method for the numerical approximation of the time-space fractional diffusion equation in an unbounded domain by using the fractional-order generalized Jacobi functions and the mapped Chebyshev functions, and theoretically prove the high convergence rate. The reason for using the fractional-order generalized Jacobi functions is to approximate the solution with singularity at the initial time. We prove that the proposed approximation scheme has a spectral convergence rate when the solution of a given problem satisfies a particular condition. We also establish the stability of the method.
Kang et al. (Thu,) studied this question.