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September 10, 2025Open Access

Existence results for nonlinear hybrid fractional differential equations with generalized Ψ, Φ-Caputo-Fabrizio derivative

Key Points

The study establishes existence and uniqueness of solutions for nonlinear fractional hybrid differential equations, enhancing foundational knowledge.
Banach's fixed point theorem is utilized to demonstrate key results within the prescribed framework of fractional analysis.
A simulation of solutions illustrates the practical utility of the theoretical findings using the Adams Bashford method.
This research contributes to the understanding of fractional dynamics and their applications in complex systems.

Abstract

The aim of this paper is to develop a theory of fractional hybrid differential equations with perturbations of second type involving ?, ? Caputo-Fabrizio fractional derivative of an arbitrary order ? ? (0, 1). We demonstrate the existence and uniqueness of solutions for a particular class of nonlinear frac-tional hybrid differential equations with initial conditions by applying Banach?s fixed point theorem and some fundamental concepts on fractional analysis. As an example, a significant case is given to illustrate the utility of our theoretical findings. We also, give a simulation of the solution by applying the Adams Bashford with three steps method.

Existence results for nonlinear hybrid fractional differential equations with generalized Ψ, Φ-Caputo-Fabrizio derivative

Key Points

Abstract

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