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Fractional Hamilton’s Canonical Equations and Poisson Theorem of Mechanical Systems with Fractional Factor

Author

Listed:
  • Linli Wang

    (School of Mathematics and Statistics, Xinxiang University, Xinxiang 453000, China)

  • Jingli Fu

    (College of Information and Control Engineering, Shandong Vocational University of Foreign Affairs, Weihai 264504, China
    Institute of Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China)

  • Liangliang Li

    (Department of Electronic Engineering, Tsinghua University, Beijing 100084, China)

Abstract

Because of the nonlocal and nonsingular properties of fractional derivatives, they are more suitable for modelling complex processes than integer derivatives. In this paper, we use a fractional factor to investigate the fractional Hamilton’s canonical equations and fractional Poisson theorem of mechanical systems. Firstly, a fractional derivative and fractional integral with a fractional factor are presented, and a multivariable differential calculus with fractional factor is given. Secondly, the Hamilton’s canonical equations with fractional derivative are obtained under this new definition. Furthermore, the fractional Poisson theorem with fractional factor is presented based on the Hamilton’s canonical equations. Finally, two examples are given to show the application of the results.

Suggested Citation

  • Linli Wang & Jingli Fu & Liangliang Li, 2023. "Fractional Hamilton’s Canonical Equations and Poisson Theorem of Mechanical Systems with Fractional Factor," Mathematics, MDPI, vol. 11(8), pages 1-13, April.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1803-:d:1120219
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    References listed on IDEAS

    as
    1. Kangle Wang, 2022. "Novel Scheme For The Fractal–Fractional Short Water Wave Model With Unsmooth Boundaries," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(09), pages 1-10, December.
    2. Kangle Wang, 2022. "Fractal Traveling Wave Solutions For The Fractal-Fractional Ablowitz–Kaup–Newell–Segur Model," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(09), pages 1-9, December.
    3. Kang-Jia Wang & Feng Shi & Guo-Dong Wang, 2022. "Periodic Wave Structure Of The Fractal Generalized Fourth-Order Boussinesq Equation Traveling Along The Non-Smooth Boundary," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(09), pages 1-8, December.
    4. Salehi, Younes & Darvishi, Mohammad T. & Schiesser, William E., 2018. "Numerical solution of space fractional diffusion equation by the method of lines and splines," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 465-480.
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