Global stability of reaction-diffusion equations with fractional Laplacian operator and applications in biology

Abstract

The main objective of this paper is to develop an efficient method to establish the global stability of some reaction-diffusion equations with fractional Laplacian operator. This method is based on Lyapunov functionals for ordinary differential equations (ODEs). A classical case of such types of fractional spacial diffusion equations is rigorously studied. Moreover, the developed method is applied to some biological systems arising from epidemiology and cancerology.