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Response characteristics of a fractional oscillator

Author

Listed:
  • Narahari Achar, B.N.
  • Hanneken, John W.
  • Clarke, T.

Abstract

The integral equation of motion of a driven fractional oscillator is obtained by generalizing the corresponding equation of motion of a driven harmonic oscillator to include integrals of arbitrary order according to the methods of fractional calculus. The Green's function solution for the fractional oscillator is obtained in terms of Mittag–Leffler functions using Laplace transforms. The response and resonance characteristics of the fractional oscillator are studied for several cases of forcing function.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:309:y:2002:i:3:p:275-288
    DOI: 10.1016/S0378-4371(02)00609-X
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    Cited by:

    1. Tian, Yan & Zhong, Lin-Feng & He, Gui-Tian & Yu, Tao & Luo, Mao-Kang & Stanley, H. Eugene, 2018. "The resonant behavior in the oscillator with double fractional-order damping under the action of nonlinear multiplicative noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 845-856.
    2. Drozdov, A.D., 2007. "Fractional oscillator driven by a Gaussian noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 237-245.
    3. Svenkeson, A. & Beig, M.T. & Turalska, M. & West, B.J. & Grigolini, P., 2013. "Fractional trajectories: Decorrelation versus friction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5663-5672.
    4. Berman, Michael & Cederbaum, Lorenz S., 2018. "Fractional driven-damped oscillator and its general closed form exact solution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 744-762.
    5. Kavyanpoor, Mobin & Shokrollahi, Saeed, 2017. "Challenge on solutions of fractional Van Der Pol oscillator by using the differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 44-45.
    6. Mishra, Shalabh Kumar & Upadhyay, Dharmendra Kumar & Gupta, Maneesha, 2018. "An approach to improve the performance of fractional-order sinusoidal oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 126-135.
    7. Balachandran, K. & Govindaraj, V. & Rivero, M. & Trujillo, J.J., 2015. "Controllability of fractional damped dynamical systems," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 66-73.

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