Global stability of travelling wave fronts for non-local diffusion equations with delay

This paper is concerned with the global stability of travelling wave fronts for non-local diffusion equations with delay. We prove that the non-critical travelling wave fronts are globally exponentially stable under perturbations in some exponentially weighted $L^\infty$-spaces. Moreover, we obtain the decay rates of $\sup_{x\in\mathbb{R}}|u(x,t)-\varphi(x+ct)|$ using weighted energy estimates.