IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v516y2026ics0096300325006101.html

Symmetry analysis and reduction of fractional nonlinear diffusion equations in visco-plastic materials

Author

Listed:
  • Zhang, Tian-Qi
  • Yun, Yin-Shan
  • Bai, Yu-Shan
  • Bai, Yan-Hong

Abstract

In this paper, the Lie symmetry analysis method is applied to study a fractional nonlinear diffusion equation (FNDE) with the Riemann-Liouville derivative that describes motion in visco-plastic materials. First, a classification theorem is provided, where the diffusion coefficient depends on the first-order spatial derivative term. These symmetries are then used to reduce the FNDE to a fractional ordinary differential equation (FODE) involving the Erdélyi-Kober fractional derivative. Finally, the Lie symmetry classification is extended to a more general equation with a spatially independent variable. The reductions achieved via Lie symmetry analysis provide a foundation for further investigation.

Suggested Citation

  • Zhang, Tian-Qi & Yun, Yin-Shan & Bai, Yu-Shan & Bai, Yan-Hong, 2026. "Symmetry analysis and reduction of fractional nonlinear diffusion equations in visco-plastic materials," Applied Mathematics and Computation, Elsevier, vol. 516(C).
    • Handle: RePEc:eee:apmaco:v:516:y:2026:i:c:s0096300325006101
    DOI: 10.1016/j.amc.2025.129885
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300325006101
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2025.129885?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Zhang, Zhi-Yong & Liu, Cheng-Bao, 2022. "Leibniz-type rule of variable-order fractional derivative and application to build Lie symmetry framework," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    2. Hejazi, S. Reza & Saberi, Elaheh & Mohammadizadeh, Fatemeh, 2021. "Anisotropic non-linear time-fractional diffusion equation with a source term: Classification via Lie point symmetries, analytic solutions and numerical simulation," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    3. Nass, Aminu M., 2019. "Lie symmetry analysis and exact solutions of fractional ordinary differential equations with neutral delay," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 370-380.
    4. Rafail K. Gazizov & Stanislav Yu. Lukashchuk, 2021. "Higher-Order Symmetries of a Time-Fractional Anomalous Diffusion Equation," Mathematics, MDPI, vol. 9(3), pages 1-10, January.
    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. Mohammadizadeh, Fatemeh & Rashidi, Saeede & Hejazi, S. Reza, 2021. "Space–time fractional Klein-Gordon equation: Symmetry analysis, conservation laws and numerical approximations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 476-497.
    2. Aminu Ma’aruf Nass, 2022. "Lie Point Symmetries of Autonomous Scalar First-Order Itô Stochastic Delay Ordinary Differential Equations," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1939-1951, September.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:eee:apmaco:v:516:y:2026:i:c:s0096300325006101. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.