An efficient difference scheme for the non-Fickian time-fractional diffusion equations with variable coefficient

Abstract In this paper, we develop an efficient difference scheme for the non-Fickian time-fractional diffusion equations with variable coefficient. This model may be considered as a generalization of the Kolmogorov–Petrovskii–Piskunov type equation, which is widely used to describe some important phenomena in the fields of chemistry, biology and viscoelastic materials. The stability and convergence of the difference scheme in the maximum norm are proved by the discrete energy method under mild conditions. A numerical example is carried out to verify our theoretical analysis results.