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Generalization of Mei symmetry approach to fractional Birkhoffian mechanics

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  • Zhang, Yi
  • Jia, Yun-Die

Abstract

The fractional Birkhoffian systems are investigated for Mei symmetry and corresponding conserved quantities. It is divided into two cases, one is standard fractional Birkhoffian systems, the other is fractional Birkhoffian systems under quasi-fractional dynamics models of El-Nabulsi type. The fractional Pfaff-Birkhoff principles are presented, and Birkhoff’s equations are deduced. Mei symmetry and its determining equations are established. Mei symmetry theorems are proved and fractional conserved quantities are obtained.

Suggested Citation

  • Zhang, Yi & Jia, Yun-Die, 2023. "Generalization of Mei symmetry approach to fractional Birkhoffian mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s096007792201150x
    DOI: 10.1016/j.chaos.2022.112971
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    References listed on IDEAS

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    1. Ding, Juan-Juan & Zhang, Yi, 2020. "Noether’s theorem for fractional Birkhoffian system of Herglotz type with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Zhang, Yi, 2019. "Lie symmetry and invariants for a generalized Birkhoffian system on time scales," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 306-312.
    3. Song, Chuan-Jing & Cheng, Yao, 2020. "Noether's theorems for nonshifted dynamic systems on time scales," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    4. Yun-Die Jia & Yi Zhang, 2021. "Fractional Birkhoffian Mechanics Based on Quasi-Fractional Dynamics Models and Its Noether Symmetry," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-17, April.
    5. EL-Nabulsi, Ahmad Rami, 2009. "Fractional action-like variational problems in holonomic, non-holonomic and semi-holonomic constrained and dissipative dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 52-61.
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    Cited by:

    1. Jin, Shi-Xin & Chen, Xiang-Wei & Li, Yan-Min, 2024. "Approximate Noether theorem and its inverse for nonlinear dynamical systems with approximate nonstandard Lagrangian," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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