Existence and uniqueness of global mild solutions for a class of nonlinear fractional reaction–diffusion equations with delay

Abstract

In this paper, we study the mild solutions of a class of nonlinear fractional reaction–diffusion equations with delay and Caputo’s fractional derivatives. By the measure of noncompactness, the theory of resolvent operators, the fixed point theorem and the Banach contraction mapping principle, we develop various theorems for the existence and uniqueness of the global mild solutions for the problem.