Existence Results of Langevin Equations with Caputo–Hadamard Fractional Operator

In this manuscript, we deal with a nonlinear Langevin fractional differential equation that involves the Caputo–Hadamard and Caputo operators, nonperiodic nonlocal integral boundary conditions. The results presented in study establish existence, uniqueness, Hyers–Ulam (HU) stability of solution to proposed equation. We achieved our main result by using Banach contraction mapping principle Krasonoselskii’s fixed point theorem. Furthermore, introduce an application demonstrate validity findings.