A Study on Some Classes of Hybrid Langevin Pantograph ψ-Caputo Fractional Coupled Systems

This paper focuses on the study of a class of coupled systems of hybrid Langevin fractional pantograph differential equations involving the ψ-Caputo fractional derivative within Banach spaces. By applying Banach’s fixed-point theorem, we demonstrate the uniqueness of solutions to our coupled system. The existence of the solution is then shown using Dhage’s fixed-point theorem. Additionally, we analyze the stability in the sense of Ulam-Hyers and Ulam-Hyers-Rassias. Finally, we present an example to illustrate our results.