Criteria of existence and stability of an n-coupled system of generalized Sturm-Liouville equations with a modified ABC fractional derivative and an application to the SEIR influenza epidemic model

The primary objective of this study was to explore the behavior of an n-coupled system of generalized Sturm-Liouville (GSL) and Langevin equations under a modified ABC fractional derivative. We aimed to analyze the dynamics of the system and gain insights into how this operator influences the conditions for the existence and uniqueness of solutions. We established the existence and uniqueness of solutions by employing the Banach contraction principle and Leray-Schauder's alternative fixed-point theorem. We also investigated the Hyers-Ulam stability of the system. This analysis allows us to understand the stability properties of the solutions and evaluate their sensitivity to perturbations. Furthermore, we employed Lagrange's interpolation polynomials to produce a numerical scheme for the influenza epidemic model. By combining theoretical analysis, mathematical principles, and numerical simulations, this study contributes to enriching our understanding of the behavior of the system and offers insights into its dynamics and practical applications in epidemiology.