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

Abstract

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 explores the stability of solutions for a coupled system of ψ– Hilfer nonlinear implicit fractional differential equations with multipoint boundary conditions in terms of Ulam–Hyers, Ulam–Hyers– Rassias, generalized Ulam–Hyers,and generalized Ulam–Hyers–Rassias stability. To demonstrate the applicability of the theoretical results, several examples are presented. More critically, the deficiency in the existing literature is covered up by the current work,which advances the understanding of these complex systems. These contributions not only deepen the theoretical understanding of fractional systems but also provide a solid foundation for future research in this dynamic field.