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Mathematical Problems in Engineering
Volume 2014, Article ID 254012, 8 pages
Research Article

Monotone Iterative Methods of Positive Solutions for Fractional Differential Equations Involving Derivatives

College of Electron and Information, Zhejiang University of Media and Communications, Hangzhou, Zhejiang 310018, China

Received 23 September 2013; Accepted 27 December 2013; Published 4 February 2014

Academic Editor: Rosana Rodriguez-Lopez

Copyright © 2014 Xiaoping Zhang and Yongping Sun. 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.


This paper studies the existence and computing method of positive solutions for a class of nonlinear fractional differential equations involving derivatives with two-point boundary conditions. By applying monotone iterative methods, the existence results of positive solutions and two iterative schemes approximating the solutions are established. The interesting point of our method is that the iterative scheme starts off with a known simple function or the zero function and the nonlinear term in the fractional differential equation is allowed to depend on the unknown function together with derivative terms. Two explicit numerical examples are given to illustrate the results.