On stability and solution criteria for coupled Langevin fractional differential equations

This article explores the existence and uniqueness of solutions for a coupled system of Langevin fractional differential equations that incorporate the Katugampola fractional integral boundary conditions. The study utilizes the Banach contraction mapping principle and the Leray-Schauder nonlinear alternative to establish criteria for existence and uniqueness. Additionally, the stability of the solutions is examined through the Hyers-Ulam stability method, providing insights into the system’s response to small changes. To validate the theoretical outcomes, a numerical example is provided, showcasing the practical application of the methods and confirming the results. These findings offer valuable insights into the behavior of fractional differential systems, with implications for various scientific and engineering applications.