Nonlocal Kernel‐Driven ΦΦ‐Caputo Fractional Integro‐Differential Systems Involving the Generalized Laplace Transform

This study explores the existence and uniqueness of solutions for a fractional integro‐differential equation of order involving a kernel operator. To construct the solution, we utilize the generalized ‐Laplace transform, which provides an explicit representation in terms of Mittag–Leffler functions and ‐convolutions. We establish the existence of solutions using Krasnoselskii's fixed point theorem, while uniqueness is proven through Banach's contraction principle. An illustrative example is included to demonstrate the applicability of our results.