IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v31y2023i03ns0218348x23500287.html
   My bibliography  Save this article

Non-Differentiable Exact Solutions Of The Local Fractional Zakharov–Kuznetsov Equation On The Cantor Sets

Author

Listed:
  • KANG-JIA WANG

    (School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China)

  • FENG SHI

    (School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China)

  • JING SI

    (School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China)

  • JING-HUA LIU

    (School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China)

  • GUO-DONG WANG

    (School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, P. R. China)

Abstract

In this study, a new fractional Zakharov–Kuznetsov equation (ZKE) within the local fractional derivative (LFD) is derived. Yang’s non-differentiable (ND) traveling wave transform is introduced, then two novel techniques namely the Mittag-Leffler function-based method (MLFBM) and Yang’s special function method (Y-SFM) are adopted to seek for the ND exact solutions for the first time. With the aid of the Mathematica software, the dynamic behaviors of the different solutions on the Cantor sets are illustrated via the 3D plots by assigning the appropriate parameters. The attained results confirm that the mentioned methods are effective and straightforward, which can be used to study the ND exact solutions of the local fractional partial differential equations (PDEs).

Suggested Citation

  • Kang-Jia Wang & Feng Shi & Jing Si & Jing-Hua Liu & Guo-Dong Wang, 2023. "Non-Differentiable Exact Solutions Of The Local Fractional Zakharov–Kuznetsov Equation On The Cantor Sets," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(03), pages 1-11.
    • Handle: RePEc:wsi:fracta:v:31:y:2023:i:03:n:s0218348x23500287
    DOI: 10.1142/S0218348X23500287
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X23500287
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X23500287?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 search for a different version of it.

    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:wsi:fracta:v:31:y:2023:i:03:n:s0218348x23500287. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Tai Tone Lim (email available below). General contact details of provider: https://www.worldscientific.com/worldscinet/fractals .

    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.