On the Existence of Solutions for ψ-Caputo Fractional Integro-Differential Boundary Value Problems

In this article, we investigate the existence of solutions for a class of fractional integro-differential equations (FIDE’s) involving the ψ-Caputo fractional derivative (ψ-CFD) subject to ψ-Caputo boundary conditions. The analysis is carried out in an appropriate Banach space setting using the Mönch fixed-point theorem. Furthermore, sufficient conditions ensuring the existence and uniqueness of solutions are derived by employing tools from nonlinear functional analysis. In addition, the obtained results contribute to the current literature by extending existing works on fractional differential equations (FDE’s) involving generalized Caputo-type operators. The novelty of this study lies in the incorporation of ψ-CFD’s together with ψ-Caputo boundary conditions under the framework of Mönch fixed-point theory. An illustrative example is provided to verify the applicability and effectiveness of the theoretical findings.