Convergence and stability of compact finite difference method for nonlinear time fractional reaction-diffusion equations with delay

This paper is concerned with numerical solutions of nonlinear time fractional reaction-diffusion equations with time delay. A linearized compact finite difference scheme is proposed to solve the equations. In terms of a new developed fractional Gronwall type inequality, convergence and stability of the proposed scheme are obtained. Numerical experiments are given to illustrate the theoretical results.