Existence and stability results for a Langevin system with Caputo–Hadamard fractional operators

Abstract

This paper is devoted to analyzing a new model of a coupled Langevin system with fractional operators under nonlocal antiperiodic integral boundary conditions. This model involves nonlinear Langevin fractional equations with Caputo–Hadamard and Caputo fractional operators. Also, the existence and uniqueness of solutions to the suggested model have been investigated by the fixed-point technique. Moreover, the Hyers–Ulam stability of the solutions has been discussed. Finally, we provide an illustrative example to support the theoretical results.

Keywords: Fixed Point Technique, Fractional Derivatives, Langevin Fractional Equation, Stability Analysis