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Abstract and Applied Analysis
Volume 2012, Article ID 423796, 24 pages
Research Article

Existence Results for Fractional Differential Inclusions with Multivalued Term Depending on Lower-Order Derivative

1School of Mathematical Science and Computing Technology, Central South University, Changsha, Hunan 410075, China
2School of Science, Guangxi University for Nationalities, Nanning, Guangxi 530006, China

Received 24 October 2012; Accepted 14 December 2012

Academic Editor: Svatoslav Staněk

Copyright © 2012 Xiaoyou Liu and Zhenhai Liu. 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.


This paper is concerned with a class of fractional differential inclusions whose multivalued term depends on lower-order fractional derivative with fractional (non)separated boundary conditions. The cases of convex-valued and non-convex-valued right-hand sides are considered. Some existence results are obtained by using standard fixed point theorems. A possible generalization for the inclusion problem with integral boundary conditions is also discussed. Examples are given to illustrate the results.