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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 -∞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.

Suggested Citation

  • Jun-Sheng Duan, 2013. "The Periodic Solution of Fractional Oscillation Equation with Periodic Input," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlamp:v:2013:y:2013:i:1:n:869484
    DOI: 10.1155/2013/869484
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    References listed on IDEAS

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    1. Narahari Achar, B.N. & Hanneken, John W. & Clarke, T., 2002. "Response characteristics of a fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(3), pages 275-288.
    2. Duan, Jun-Sheng & Wang, Zhong & Liu, Yu-Lu & Qiu, Xiang, 2013. "Eigenvalue problems for fractional ordinary differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 46(C), pages 46-53.
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