Ulam-Hyers-Rassias stability results for a coupled system of ψ-Hilfer nonlinear implicit fractional differential equations with multipoint boundary conditions

Over the past decade, significant progress has been made in the stability analysis of nonlinear systems. However, coupled systems of nonlinear problems remain largely unexplored in the literature. This paper investigates the stability properties of solutions for a coupled system of ?-Hilfer nonlinear implicit fractional differential equations with multipoint boundary conditions over a finite interval. The stability analysis is conducted in terms of Ulam-Hyers, Ulam-Hyers-Rassias, generalized Ulam-Hyers, and generalized Ulam-Hyers-Rassias stability. The approach employs analytical techniques specifically designed for fractional differential equations, providing a rigorous evaluation of stability under different perturbations. To demonstrate the applicability of the proposed theoretical framework, several illustrative examples are provided, showcasing how the stability conditions are satisfied in practical scenarios. These examples offer valuable insights into the behavior of solutions under different parameter settings, emphasizing the robustness of the obtained stability results. More critically, this study fills a fundamental gap in the literature by extending stability analysis to coupled nonlinear implicit fractional systems. The findings contribute to a deeper theoretical understanding of fractional-order models and provide a solid foundation for future research in this evolving domain. Additionally, the results have significant implications for applications in various scientific and engineering disciplines, including control theory, mathematical biol-ogy, and signal processing, where fractional differential equations play a crucial role in modeling complex dynamical systems.