Baghani, HamidNieto Roig, Juan José2020-03-312020-03-312019Baghani H. and Nieto J. (2019) “On fractional Langevin equation involving two fractional orders in different intervals”, Nonlinear Analysis: Modelling and Control, 24(6), 884–897. doi: 10.15388/NA.2019.6.31392-5113http://hdl.handle.net/10347/21023In this paper, we study a nonlinear Langevin equation involving two fractional orders α ∈ (0; 1] and β ∈ (1; 2] with initial conditions. By means of an interesting fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for the fractional equations. Some illustrative numerical examples are also discussedeng© 2019 Authors. Published by Vilnius University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution Licence which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are creditedhttps://creativecommons.org/licenses/by/4.0/Caputo fractional derivativeInitial boundary conditionsExistence and uniquenessFractional Langevin equationjournal article10.15388/NA.2019.6.32335-8963open access