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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 745674, 8 pages
http://dx.doi.org/10.1155/2013/745674
Research Article

A Mixed Monotone Operator Method for the Existence and Uniqueness of Positive Solutions to Impulsive Caputo Fractional Differential Equations

1Basic Course Department, Business College of Shanxi University, Taiyuan, Shanxi 030031, China
2School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China

Received 10 July 2013; Accepted 8 October 2013

Academic Editor: Jehad Alzabut

Copyright © 2013 Jieming Zhang et al. 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 establish some sufficient conditions for the existence and uniqueness of positive solutions to a class of initial value problem for impulsive fractional differential equations involving the Caputo fractional derivative. Our analysis relies on a fixed point theorem for mixed monotone operators. Our result can not only guarantee the existence of a unique positive solution but also be applied to construct an iterative scheme for approximating it. An example is given to illustrate our main result.