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