On nonlocal integral and derivative boundary value problem of nonlinear Hadamard Langevin equation with three different fractional orders

Abstract

This paper is concerned with Hadamard fractional Langevin differential equation subject to fractional integral and derivative boundary conditions and which involves three different fractional orders. By using Schaefer’s fixed point theorem and Banach contraction principle, existence and uniqueness results of solutions for the proposed equation are obtained. An example demonstrating the consistency to the theoretical findings is also presented.