Existence and Uniqueness of Boundary Value Problems for Nonlinear Hybrid Differential Equations with ABC-Fractional Derivative

Abstract

In this paper, we establish the existence and uniqueness of solutions to nonlinear hybrid fractional differential equations within the Atangana-Baleanu-Caputo framework. Our analysis incorporates both linear and nonlinear perturbations. The proposed method relies on the nonlinear Leray-Schauder alternative in combination with Banach’s fixed-point theorem, ensuring a robust mathematical foundation. To illustrate the practical significance of our findings, we provide a concrete example that demonstrates their applicability.