Existence and Ulam Stability Results of Hybrid Langevin Pantograph $\psi$-Fractional Coupled Systems

Abstract

This study presents results on the solutions of a coupled system of hybrid Langevin fractional pantograph differential equations involving $\psi$-Caputo fractional derivatives within Banach spaces. We establish the uniqueness of solutions using Banach's fixed-point theorem and confirm their existence through Dhage's hybrid fixed-point theorem for the sum of three operators. Additionally, we investigate the stability of these solutions in both the Ulam-Hyers sense and its generalized form. The theoretical findings are further supported by several illustrative examples.