IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i8p1803-d1120219.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/8/1803/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/8/1803/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Darvishi, M.T. & Najafi, Mohammad & Wazwaz, Abdul-Majid, 2021. "Conformable space-time fractional nonlinear (1+1)-dimensional Schrödinger-type models and their traveling wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Chaudhary, Manish & Kumar, Rohit & Singh, Mritunjay Kumar, 2020. "Fractional convection-dispersion equation with conformable derivative approach," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    3. Kholoud Saad Albalawi & Ibtehal Alazman & Jyoti Geetesh Prasad & Pranay Goswami, 2023. "Analytical Solution of the Local Fractional KdV Equation," Mathematics, MDPI, vol. 11(4), pages 1-13, February.
    4. Liu, Lu & Xue, Dingyu & Zhang, Shuo, 2019. "Closed-loop time response analysis of irrational fractional-order systems with numerical Laplace transform technique," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 133-152.
    5. Vargas, Antonio M., 2022. "Finite difference method for solving fractional differential equations at irregular meshes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 204-216.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1803-:d:1120219. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.