Existence and Uniqueness of Boundary Value Problems involving Nonlinear Hybrid Differential Equations with Caputo–Fabrizio Fractional Derivative

Abstract

This paper investigates the existence and uniqueness of solutions for boundary value problems involving nonlinear hybrid differential equations with the Caputo–Fabrizio fractional derivative. By employing fixed–point theorems such as Banach’s contraction principle, we establish sufficient conditions ensuring the well–posedness of the problem. The analysis leverages the non–singular and non–local properties of the Caputo–Fabrizio derivative to model complex dynamical systems more effectively. An example and numerical scheme are provided to illustrate the theoretical findings.