Finite difference method for Riesz space fractional diffusion equations with delay and a nonlinear source term

In this paper, we propose a finite difference method for the Riesz space fractional diffusion equations with delay and a nonlinear source term on a finite domain. The proposed method combines a time scheme based on the predictor-corrector method and the Crank-Nicolson scheme for the spatial discretization. The corresponding theoretical results including stability and convergence are provided. Some numerical examples are presented to validate the proposed method.