Journal of Applied Mathematics
Volume 2012 (2012), Article ID 691651, 13 pages
http://dx.doi.org/10.1155/2012/691651
Research Article

Positive Mild Solutions of Periodic Boundary Value Problems for Fractional Evolution Equations

Jia Mu1,2 and Hongxia Fan2

1School of Mathematics and Computer Science Institute, Northwest University for Nationalities, Gansu, Lanzhou 730000, China
2Department of Mathematics, Northwest Normal University, Gansu, Lanzhou 730000, China

Received 29 October 2011; Accepted 14 February 2012

Academic Editor: Shiping Lu

Copyright © 2012 Jia Mu and Hongxia Fan. 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

The periodic boundary value problem is discussed for a class of fractional evolution equations. The existence and uniqueness results of mild solutions for the associated linear fractional evolution equations are established, and the spectral radius of resolvent operator is accurately estimated. With the aid of the estimation, the existence and uniqueness results of positive mild solutions are obtained by using the monotone iterative technique. As an application that illustrates the abstract results, an example is given.