Abstract
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 timetwith the same circular frequency as the input, and the frequency of the solution is not affected by the system frequencycas 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.