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Challenge on solutions of fractional Van Der Pol oscillator by using the differential transform method

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  • Kavyanpoor, Mobin
  • Shokrollahi, Saeed

Abstract

In this letter, a solution of the fractional Van Der Pol equation that uses the differential transform method has been investigated. In previous studies this method was incorrectly applied to the fractional Van Der Pol oscillator and inaccurate results were obtained. In this note, true solution of the problem has been presented. Although it was shown that, this method is not appropriate and a non-periodic solution was obtained.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:98:y:2017:i:c:p:44-45
    DOI: 10.1016/j.chaos.2017.03.028
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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. Arikoglu, Aytac & Ozkol, Ibrahim, 2007. "Solution of fractional differential equations by using differential transform method," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1473-1481.
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    Cited by:

    1. Li, Wei & Huang, Dongmei & Zhang, Meiting & Trisovic, Natasa & Zhao, Junfeng, 2019. "Bifurcation control of a generalized VDP system driven by color-noise excitation via FOPID controller," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 30-38.
    2. Sahadevan, R. & Prakash, P., 2017. "On Lie symmetry analysis and invariant subspace methods of coupled time fractional partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 107-120.

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