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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 428793, 7 pages
http://dx.doi.org/10.1155/2013/428793
Research Article

Positive Solutions for the Initial Value Problem of Fractional Evolution Equations

1Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
2Science College, Gansu Agricultural University, Lanzhou 730070, China

Received 9 December 2012; Accepted 19 February 2013

Academic Editor: Changbum Chun

Copyright © 2013 He Yang and Yue Liang. 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

By using the fixed point theorems and the theory of analytic semigroup, we investigate the existence of positive mild solutions to the Cauchy problem of Caputo fractional evolution equations in Banach spaces. Some existence theorems are obtained under the case that the analytic semigroup is compact and noncompact, respectively. As an example, we study the partial differential equation of the parabolic type of fractional order.