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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 903518, 15 pages
http://dx.doi.org/10.1155/2012/903518
Research Article

Existence of Mild Solutions for a Class of Fractional Evolution Equations with Compact Analytic Semigroup

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 2 May 2012; Revised 9 September 2012; Accepted 27 September 2012

Academic Editor: Dumitru Bǎleanu

Copyright © 2012 He Yang. 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

This paper deals with the existence of mild solutions for a class of fractional evolution equations with compact analytic semigroup. We prove the existence of mild solutions, assuming that the nonlinear part satisfies some local growth conditions in fractional power spaces. An example is also given to illustrate the applicability of abstract results.