Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 657839, 9 pages
doi:10.1155/2011/657839
Research Article

Exact Solution of Impulse Response to a Class of Fractional Oscillators and Its Stability

1School of Information Science and Technology, East China Normal University, no. 500, Dong-Chuan Road, Shanghai 200241, China
228 Farrer Road, #05-01, Sutton Place, 268831, Singapore
3College of Computer Science, Zhejiang University of Technology, Hangzhou 310023, China

Received 18 August 2010; Accepted 15 September 2010

Academic Editor: Cristian Toma

Copyright © 2011 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.

Abstract

Oscillator of single-degree-freedom is a typical model in system analysis. Oscillations resulted from differential equations with fractional order attract the interests of researchers since such a type of oscillations may appear dramatic behaviors in system responses. However, a solution to the impulse response of a class of fractional oscillators studied in this paper remains unknown in the field. In this paper, we propose the solution in the closed form to the impulse response of the class of fractional oscillators. Based on it, we reveal the stability behavior of this class of fractional oscillators as follows. A fractional oscillator in this class may be strictly stable, nonstable, or marginally stable, depending on the ranges of its fractional order.