Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis and College of Sciences, Guangxi University for Nationalities, Nanning, Guangxi 530006, China
Copyright © 2013 Jing Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study a boundary value problem for fractional equations involving two fractional orders. By means of a fixed point theorem, we establish sufficient conditions for the existence and uniqueness of solutions for the fractional equations. In addition, we describe the dynamic behaviors of the fractional Langevin equation by using the algorithm.