A generalized Laguerre spectral Petrov–Galerkin method for the time-fractional subdiffusion equation on the semi-infinite domain

In this paper, a generalized Laguerre spectral Petrov–Galerkin method is proposed to solve a class of time-fractional subdiffusion equations on the semi-infinite domain. We use the generalized associated Laguerre functions of the first kind and the generalized Laguerre functions as basis functions in time and space directions separately. The respective projection error estimates can be obtained as well. We derive the projection error estimates of the solutions in time-space directions. The approximation results of the fully discrete spectral scheme are introduced in this paper. Some numerical results are presented to illustrate the efficiency of this method.