Existence of Solution for a Coupled System of Langevin Equations Involving the ψ$$ \psi $$‐Hilfer Fractional Derivative

ABSTRACT This paper is devoted to the study of a coupled system of fractional Langevin equations involving the ‐Hilfer fractional derivative and nonlocal Riemann–Stieltjes integral boundary conditions. By transforming the problem into an equivalent system of integral equations, sufficient conditions for the existence of solutions are established via Schauder's fixed point theorem and the Leray–Schauder nonlinear alternative. In addition, uniqueness results are obtained by applying the Banach contraction principle. Several illustrative examples are provided to demonstrate the applicability of the theoretical results and to validate the proposed approach.