Abstract
In this paper, we discuss the existence of a unique solution of Caputo-Liouville type Langevin equation involving two fractional orders and finitely many nonlinearities, equipped with nonlocal boundary conditions via Banach contraction mapping principle. The location of the unique solution of the given problem is also presented. In addition, we discuss the existence of solutions for the problem at hand by means of Krasnosel'skii's fixed point theorem. Examples are constructed for the illustration of the obtained results. The paper concludes with some interesting remarks.