# The Periodic Solution of Fractional Oscillation Equation with Periodic Input

*Jun-Sheng Duan* ()

*Advances in Mathematical Physics*, 2013, vol. 2013, 1-6

**Abstract:**
The periodic solution of fractional oscillation equation with periodic input is considered in this work. The fractional derivative operator is taken as , 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.

**Date:** 2013

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**Persistent link:** https://EconPapers.repec.org/RePEc:hin:jnlamp:869484

**DOI:** 10.1155/2013/869484

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