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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 267108, 12 pages
http://dx.doi.org/10.1155/2012/267108
Research Article

Existence Results for Solutions of Nonlinear Fractional Differential Equations

1Department of Statistics, Gaziosmanpasa University, 60250 Tokat, Turkey
2Department of Primary Mathematics Education, Mevlana University, 34528 Konya, Turkey

Received 15 February 2012; Accepted 1 April 2012

Academic Editor: Allaberen Ashyralyev

Copyright © 2012 Ali Yakar and Mehmet Emir Koksal. 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 deals with theoretical and constructive existence results for solutions of nonlinear fractional differential equations using the method of upper and lower solutions which generate a closed set. The existence of solutions for nonlinear fractional differential equations involving Riemann-Liouville differential operator in a closed set is obtained by utilizing various types of coupled upper and lower solutions. Furthermore, these results are extended to the finite systems of nonlinear fractional differential equations leading to more general results.