Integro-differential equations implicated with Caputo-Hadamard derivatives under nonlocal boundary constraints

Abstract

Abstract The goal of this work is to derive a new type of fractional system that arises from the combination of the Caputo-Hadamard derivative with the integro-differential equation. Also, the existence and uniqueness of solutions to this problem have been studied under nonlocal boundary conditions. Moreover, Hyer-Ulam stability has been studied for the considered problem. Finally, to reinforce the theoretical results and provide applications for our paper, two supporting examples have been emphasized.