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Mathematical Problems in Engineering
Volume 2012, Article ID 746872, 16 pages
http://dx.doi.org/10.1155/2012/746872
Research Article

Periodic Boundary Value Problems for Semilinear Fractional Differential Equations

Department of Mathematics, Northwest Normal University, Lanzhou, Gansu 730000, China

Received 27 September 2011; Accepted 5 December 2011

Academic Editor: Kwok W. Wong

Copyright © 2012 Jia Mu and Yongxiang Li. 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 study the periodic boundary value problem for semilinear fractional differential equations in an ordered Banach space. The method of upper and lower solutions is then extended. The results on the existence of minimal and maximal mild solutions are obtained by using the characteristics of positive operators semigroup and the monotone iterative scheme. The results are illustrated by means of a fractional parabolic partial differential equations.