Fixed Point Approach for Fractional Order Differential Equation Systems

Year 2025, Volume: 14 Issue: 2, 124 - 137, 31.08.2025

Lale Cona , Alperen Hasan Kocağ

https://doi.org/10.54187/jnrs.1671939

Abstract

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.

Keywords

Atangana-Baleanu Caputo fraction order derivative , initial value problem , fraction order differential equation systems , fixed point theorem

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