The Periodic Solution of Fractional Oscillation Equation with Periodic Input

Jun-Sheng Duan

Advances in Mathematical Physics, 2013, vol. 2013, issue 1

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 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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https://doi.org/10.1155/2013/869484

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2013:y:2013:i:1:n:869484

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