Langevin equation involving one fractional order with threepoint boundary conditions

In this paper, we investigate a class of nonlinear Langevin equation involving one fractional order \(\alpha\in(0, 1]\) with threepoint boundary conditions. By the Banach contraction principle and Krasnoselskii s fixed point theorem, the existence and uniqueness results of solutions are obtained. Two examples are given to show the applicability of our main results.