Existence and uniqueness of the solutions for a nonlinear time-conformable fractional reaction-diffusion equations with delay

Abstract

In this work, two coupled systems for nonlinear time-conformable fractional reaction-diffusion equation with delay have been considered. Under some hypotheses in given data we have proved first the existence of the solution for both systems by using Leary-Schauder fixed point theorem. After, we have showed the uniqueness of the solution for the same two systems by using the contraction mapping theorem.