Existence of solutions and Hyers-Ulam stability for a coupled system of nonlinear Langevin equations involving φ-Riemann-Liouville and ψ-Caputo fractional derivatives subject to mixed boundary conditions

Abstract

This work investigates the existence, uniqueness, and Hyers-Ulam Stability of solutions to a class of coupled system of nonlinear Langevin equations involving mixed generalized fractional derivatives. The system under consideration is governed by the φ -Caputo and Ψ-Riemann-Liouville fractional operators, subject to mixed boundary conditions. After presenting the necessary prelimi-naries and definitions within the framework of generalized fractional calculus, we employ fixed point theorems to establish sufficient conditions for the existence and uniqueness of solutions. Additionally, Hyers-Ulam stability of the system is investigated. Two pertinent examples are provided to verify the validity of the reported theoretical results.