Characteristic Roots of a Class of Fractional Oscillators-Reference-Cited by-同舟云学术

Characteristic Roots of a Class of Fractional Oscillators

Published:2013 Issue: Volume:2013 Page:1-7
ISSN:1687-7357
Container-title:Advances in High Energy Physics
language:en
Short-container-title:Advances in High Energy Physics

Author:

Li Ming¹²^ORCID,Lim S. C.³,Cattani Carlo⁴,Scalia Massimo⁵

Affiliation:

1. School of Information Science & Technology, East China Normal University No. 500, Dong-Chuan Road, Shanghai 200241, China

2. Department of Computer and Information Science, University of Macau, Avenue Padre Tomas Pereira, Taipa 1356, Macau SAR, China

3. Faculty of Engineering, Multimedia University, Selangor Darul Ehsan, 63100 Cyberjaya, Malaysia

4. Department of Mathematics, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy

5. Department of Mathematics, University of Rome, la Sapienza Piazzale Aldo Moro, 00185 Rome, Italy

Abstract

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.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Nuclear and High Energy Physics

Link

http://downloads.hindawi.com/journals/ahep/2013/853925.pdf

Reference80 articles.

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