Fixed Point Approach for Fractional Order Differential Equation Systems

This paper examines the existence and uniqueness of solutions to a nonlinear system of fractional differential equations involving the Atangana–Baleanu fractional derivative. The system under consideration is analyzed through a fixed-point approach by means of the Perov sense. The Atangana–Baleanu fractional derivative, characterized by a non-local and non-singular kernel, provides a more suitable framework for modeling various physical phenomena. The main results are illustrated through an example, which demonstrates the applicability and reliability of the proposed approach.