Abstract and Applied Analysis
Volume 2013 (2013), Article ID 869837, 17 pages
http://dx.doi.org/10.1155/2013/869837
Research Article

Existence Results for Langevin Fractional Differential Inclusions Involving Two Fractional Orders with Four-Point Multiterm Fractional Integral Boundary Conditions

Ahmed Alsaedi,1 Sotiris K. Ntouyas,2 and Bashir Ahmad1

1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
2Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Received 2 January 2013; Accepted 22 March 2013

Academic Editor: Juan J. Nieto

Copyright © 2013 Ahmed Alsaedi 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.

Abstract

We discuss the existence of solutions for Langevin fractional differential inclusions involving two fractional orders with four-point multiterm fractional integral boundary conditions. Our study relies on standard fixed point theorems for multivalued maps and covers the cases when the right-hand side of the inclusion has convex as well as nonconvex values. Illustrative examples are also presented.