The Periodic Solution of Fractional Oscillation Equation with Periodic Input
Author
Source
Advances in Mathematical Physics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-09-29
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
The periodic solution of fractional oscillation equation with periodic input is considered in this work.
The fractional derivative operator is taken as -∞Dtα, where the initial time is -∞; hence, initial conditions are not needed in the model of the present fractional oscillation equation.
With the input of the harmonic oscillation, the solution is derived to be a periodic function of time t with the same circular frequency as the input, and the frequency of the solution is not affected by the system frequency c as is affected in the integer-order case.
These results are similar to the case of a damped oscillation with a periodic input in the integer-order case.
Properties of the periodic solution are discussed, and the fractional resonance frequency is introduced.
American Psychological Association (APA)
Duan, Jun-Sheng. 2013. The Periodic Solution of Fractional Oscillation Equation with Periodic Input. Advances in Mathematical Physics،Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-504844
Modern Language Association (MLA)
Duan, Jun-Sheng. The Periodic Solution of Fractional Oscillation Equation with Periodic Input. Advances in Mathematical Physics No. 2013 (2013), pp.1-6.
https://search.emarefa.net/detail/BIM-504844
American Medical Association (AMA)
Duan, Jun-Sheng. The Periodic Solution of Fractional Oscillation Equation with Periodic Input. Advances in Mathematical Physics. 2013. Vol. 2013, no. 2013, pp.1-6.
https://search.emarefa.net/detail/BIM-504844
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-504844