Study of subdiffusion equation with different fractional derivative and their analysis

Abstract

In this paper, we obtained a solution of the fractional subdiffusion equation with initial and boundary conditions. The fractional derivative is of type Caputo, Caputo-Fabrizio, and Atangana-Baleanu-Caputo sense. Furthermore, we developed the Crank-Nicolson finite difference method to obtain a numerical solution for the subdiffusion equation. We compare numerical solutions obtained by using various fractional derivatives and representing graphically by using Python software. Also, we discussed the stability and convergence of the scheme.