A coupled system of nonlinear Caputo–Hadamard Langevin equations associated with nonperiodic boundary conditions

Abstract

In this paper, we study the coupled system of nonlinear Langevin equations involving Caputo–Hadamard fractional derivative and subject to nonperiodic boundary conditions. The existence, uniqueness, and stability in the sense of Ulam are established for the proposed system. Our approach is based on the features of the Hadamard fractional derivative, the implementation of fixed point theorems, and the employment of Urs's stability approach. An example is introduced to facilitate the understanding of the theoretical findings.