Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 425408, 16 pages
http://dx.doi.org/10.1155/2012/425408
Research Article

Positive Solution of a Nonlinear Fractional Differential Equation Involving Caputo Derivative

Changyou Wang,1,2,3 Haiqiang Zhang,2 and Shu Wang3

1College of Mathematics and Physics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2Key Laboratory of Industrial Internet of Things & Networked Control of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
3College of Applied Sciences, Beijing University of Technology, Beijing 100124, China

Received 13 August 2012; Accepted 5 September 2012

Academic Editor: Seenith Sivasundaram

Copyright © 2012 Changyou Wang 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

This paper is concerned with a nonlinear fractional differential equation involving Caputo derivative. By constructing the upper and lower control functions of the nonlinear term without any monotone requirement and applying the method of upper and lower solutions and the Schauder fixed point theorem, the existence and uniqueness of positive solution for the initial value problem are investigated. Moreover, the existence of maximal and minimal solutions is also obtained.