Existence and stability results for implicit Caputo-tempered fractional delay integro-differential equations

Abstract

We aim to study a class of implicit Caputo-tempered fractional integro-differential equations with retarded and advanced delays in Banach spaces with nonlocal conditions. By applying Sadovskii's fixed point theorem and measure of noncompactness under suitable assumptions, we establish sufficient conditions for the existence of solutions to the proposed fractional integro-differential equations in Banach spaces under nonlocal conditions. Furthermore, we prove that the solution is Hyers-Ulam stable. These results also provide a significant expansion of the existing literature in this field. Finally, an example is provided to illustrate the main results.