Nonlinear dynamics of the complex periodic coupled system via a proportional generalized fractional derivative

Abstract

The objective of this work is to study the complex dynamics of a class of nonlinear periodic coupled systems, incorporating the novel concept of the proportional fractional generalized derivative. The main contributions include establishing and deriving sufficient criteria for the existence, uniqueness, and stability of solutions for the Caputo generalized proportional fractional derivative-based periodic coupled system, representing a significant advancement in the field of fractional-order systems. The study employs the Banach contraction mapping principle and the Leray-Schauder alternative to ensure the well-posedness of the system and presents a detailed mathematical analysis to discuss the stability outcomes. To enhance the comprehension of the findings, a concrete example is provided to showcase the versatility and practical applicability of the Caputo generalized proportional fractional derivative-based periodic coupled system, highlighting the novelty and impact of this research.