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Journal of Function Spaces and Applications
Volume 2013, Article ID 518306, 16 pages
Research Article

Existence and Controllability Results for Nonlocal Fractional Impulsive Differential Inclusions in Banach Spaces

1School of Mathematics and Computer Science, Guizhou Normal College, Guiyang, Guizhou 550018, China
2Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China
3Department of Mathematical, Faculty of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia

Received 24 May 2013; Accepted 5 August 2013

Academic Editor: Henryk Hudzik

Copyright © 2013 JinRong Wang and Ahmed G. Ibrahim. 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 firstly deal with the existence of mild solutions for nonlocal fractional impulsive semilinear differential inclusions involving Caputo derivative in Banach spaces in the case when the linear part is the infinitesimal generator of a semigroup not necessarily compact. Meanwhile, we prove the compactness property of the set of solutions. Secondly, we establish two cases of sufficient conditions for the controllability of the considered control problems.