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International Journal of Differential Equations
Volume 2013 (2013), Article ID 490673, 9 pages
http://dx.doi.org/10.1155/2013/490673
Research Article

Nonlocal Problems for Fractional Differential Equations via Resolvent Operators

1Department of Mathematics, Changshu Institute of Technology, Suzhou, Jiangsu 215500, China
2Laboratoire CEREGMIA, Université des Antilles et de la Guyane, Campus Fouillole, Guadeloupe (FWI) 97159 Pointe-à-Pitre, France

Received 7 April 2013; Accepted 15 May 2013

Academic Editor: Sotiris Ntouyas

Copyright © 2013 Zhenbin Fan and Gisèle Mophou. 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 continuity of analytic resolvent in the uniform operator topology and then obtain the compactness of Cauchy operator by means of the analytic resolvent method. Based on this result, we derive the existence of mild solutions for nonlocal fractional differential equations when the nonlocal item is assumed to be Lipschitz continuous and neither Lipschitz nor compact, respectively. An example is also given to illustrate our theory.