Advances in Difference Equations
Volume 2010 (2010), Article ID 938180, 12 pages
doi:10.1155/2010/938180
Research Article

Limit Cycles of a Class of Hilbert's Sixteenth Problem Presented by Fractional Differential Equations

G. H. Erjaee,1,2 H. R. Z. Zangeneh,3 and N. Nyamoradi3

1Mathematics Department, Qatar University, Doha 2713, Qatar
2Mathematics Department, Shiraz University, Shiraz 13797-71467, Iran
3Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran

Received 21 June 2009; Accepted 15 March 2010

Academic Editor: Mouffak Benchohra

Copyright © 2010 G. H. Erjaee 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

The second part of Hilbert's sixteenth problem concerned with the existence and number of the limit cycles for planer polynomial differential equations of degree n. In this article after a brief review on previous studies of a particular class of Hilbert's sixteenth problem, we will discuss the existence and the stability of limit cycles of this class in the form of fractional differential equations.