IDEAS home Printed from https://ideas.repec.org/a/spr/indpam/v56y2025i2d10.1007_s13226-023-00495-y.html
   My bibliography  Save this article

The solution of the time-space fractional diffusion equation based on the Chebyshev collocation method

Author

Listed:
  • Junsheng Duan

    (Shanghai Institute of Technology)

  • Lixia Jing

    (Shanghai Institute of Technology)

Abstract

In this paper, we consider the solution of the initial and boundary value problem for the time-space fractional diffusion equation in the sense of Caputo based on the Chebyshev collocation method. Firstly, the problem is converted to an initial value problem for a fractional integral-differential equation which absorbs the boundary conditions. Then the shifted Chebyshev polynomials and collocation method for the space variable are used. The coefficient functions of the Chebyshev expansion are solved through the Picard iterative process and the matrix Mittag-Leffler functions for the time variable. We also present a numerical method to cope with the improper convolution integral on the time variable. Finally, a numerical example is verified via the proposed method. The results demonstrate the effectiveness and great potential of the Chebyshev polynomials and the matrix Mittag-Leffler functions for the solution of the fractional differential equation.

Suggested Citation

  • Junsheng Duan & Lixia Jing, 2025. "The solution of the time-space fractional diffusion equation based on the Chebyshev collocation method," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(2), pages 489-498, June.
    • Handle: RePEc:spr:indpam:v:56:y:2025:i:2:d:10.1007_s13226-023-00495-y
    DOI: 10.1007/s13226-023-00495-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13226-023-00495-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13226-023-00495-y?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:spr:indpam:v:56:y:2025:i:2:d:10.1007_s13226-023-00495-y. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.