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The Periodic Solution of Fractional Oscillation Equation with Periodic Input

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  • Jun-Sheng Duan

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.

Suggested Citation

  • Jun-Sheng Duan, 2013. "The Periodic Solution of Fractional Oscillation Equation with Periodic Input," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-6, September.
    • Handle: RePEc:hin:jnlamp:869484
    DOI: 10.1155/2013/869484
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