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Fractional Relativistic Yamaleev Oscillator Model and Its Dynamical Behaviors

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Abstract

In the paper we construct a new kind of fractional dynamical model, i.e. the fractional relativistic Yamaleev oscillator model, and explore its dynamical behaviors. We will find that the fractional relativistic Yamaleev oscillator model possesses Lie algebraic structure and satisfies generalized Poisson conservation law. We will also give the Poisson conserved quantities of the model. Further, the relation between conserved quantities and integral invariants of the model is studied and it is proved that, by using the Poisson conserved quantities, we can construct integral invariants of the model. Finally, the stability of the manifold of equilibrium states of the fractional relativistic Yamaleev oscillator model is studied. The paper provides a general method, i.e. fractional generalized Hamiltonian method, for constructing a family of fractional dynamical models of an actual dynamical system.

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Acknowledgments

The authors are very grateful to Editor in Chief Gerard’t Hooft and all Reviewers for their valuable comments and suggestions, which have undoubtedly improved our manuscript.

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Authors and Affiliations

  1. Institute of Theoretical Physics, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Shao-Kai Luo, Jin-Man He, Yan-Li Xu & Xiao-Tian Zhang

  2. Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou, 310018, China

    Shao-Kai Luo, Jin-Man He, Yan-Li Xu & Xiao-Tian Zhang

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  1. Shao-Kai Luo
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  2. Jin-Man He
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  3. Yan-Li Xu
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  4. Xiao-Tian Zhang
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Correspondence to Shao-Kai Luo.

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Luo, SK., He, JM., Xu, YL. et al. Fractional Relativistic Yamaleev Oscillator Model and Its Dynamical Behaviors. Found Phys 46, 776–786 (2016). https://doi.org/10.1007/s10701-015-9984-4

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  • DOI: https://doi.org/10.1007/s10701-015-9984-4

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