A Fractional Analog of Crank–Nicholson Method for the Two Sided Space Fractional Partial Equation with Functional Delay

Abstract

For two sided space fractional diffusion equation with time functional after-effect, an implicit numerical method is constructed and the order of its convergence is obtained. The method is a fractional analogue of the Crank–Nicholson method, and also uses interpolation and extrapolation of the prehistory of model with respect to time.