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September 10, 2025Journal of New Results in Science0 citationsOpen Access

Fixed Point Approach for Fractional Order Differential Equation Systems

Key Points

Uniqueness and existence of solutions are established for a nonlinear system using the fixed point approach.
The main technique employed is the Perov sense, which offers a novel way to analyze fractional differential equations.
The Atangana–Baleanu fractional derivative allows for modeling that incorporates a non-local kernel effectively.
An example demonstrates the applicability of the method, underscoring its reliability in practical applications.

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.

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CONA et al. (Sun,) studied this question.

synapsesocial.com/papers/68c18bf99b7b07f3a06141e8 https://doi.org/https://doi.org/10.54187/jnrs.1671939

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