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Advances in High Energy Physics
Volume 2013, Article ID 853925, 7 pages
Research Article

Characteristic Roots of a Class of Fractional Oscillators

1School of Information Science & Technology, East China Normal University No. 500, Dong-Chuan Road, Shanghai 200241, China
2Department of Computer and Information Science, University of Macau, Avenue Padre Tomas Pereira, Taipa 1356, Macau SAR, China
3Faculty of Engineering, Multimedia University, Selangor Darul Ehsan, 63100 Cyberjaya, Malaysia
4Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy
5Department of Mathematics, University of Rome, la Sapienza Piazzale Aldo Moro, 00185 Rome, Italy

Received 9 August 2013; Accepted 13 September 2013

Academic Editor: Gongnan Xie

Copyright © 2013 Ming Li 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.


The fundamental theorem of algebra determines the number of characteristic roots of an ordinary differential equation of integer order. This may cease to be true for a differential equation of fractional order. The results given in this paper suggest that the number of the characteristic roots of a class of oscillators of fractional order may in general be infinitely great. Further, we infer that it may also be the case for the characteristic roots of a differential equation of fractional order greater than 1. The relationship between the range of the fractional order and the locations of characteristic roots of oscillators in the complex plane is considered.