ON THE SOLVABILITY OF A NONLINEAR LANGEVIN EQUATION INVOLVING TWO FRACTIONAL ORDERS IN DIFFERENT INTERVALS

Abstract

This paper deals with a nonlinear Langevin equation involving two fractional orders with three-point boundary conditions. Our aim is to find the existence of solutions for the proposed Langevin equation by using the Banach contraction mapping principle and the Krasnoselskii’s fixed point theorem. Three examples are also given to show the significance of our results.