Fractional Langevin equations with multi-point and non-local integral boundary conditions

Abstract In this paper, we investigate a non-linear Langevin equation with periodic, multi-point and non-local fractional integral boundary conditions. The contraction mapping theorem is employed to determine sufficient conditions for the uniqueness of the solution. Also, different results in the existence of solution are demonstrated by using Krasnoselskii and Leray-Schauder theorems. Finally, some examples are provided as applications of the theorems in order to support the main outcomes of this paper.