IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i17p2718-d1731154.html
   My bibliography  Save this article

Numerical Solutions of Fractional Weakly Singular Two-Dimensional Partial Volterra Integral Equations Using Euler Wavelets

Author

Listed:
  • Seyed Sadegh Gholami

    (Department of Mathematics Education, Farhangian University, Tehran 14665-889, Iran)

  • Ali Ebadian

    (Department of Mathematics, Faculty of Science, Urmia University, Urmia 57179-44514, Iran)

  • Amirahmad Khajehnasiri

    (Department of Mathematics, Faculty of Science, Urmia University, Urmia 57179-44514, Iran)

  • Kareem T. Elgindy

    (Department of Mathematics and Sciences, College of Humanities and Sciences, Ajman University, Ajman P.O. Box 346, United Arab Emirates
    Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman P.O. Box 346, United Arab Emirates)

Abstract

This paper presents an innovative numerical method for solving two-dimensional weakly singular Volterra integral equations, including fractional Volterra integral equations with weak singularities. Solving these equations in higher dimensions and in the presence of fractional and weak singularities is highly challenging. The proposed approach uses Euler wavelets (EWs) within an operational matrix (OM) framework combined with advanced numerical techniques, initially transforming these equations into a linear algebraic system and then solving it efficiently. This method offers very high accuracy, strong computational efficiency, and simplicity of implementation, making it suitable for a wide range of such complex problems, especially those requiring high speed and precision in the presence of intricate features.

Suggested Citation

  • Seyed Sadegh Gholami & Ali Ebadian & Amirahmad Khajehnasiri & Kareem T. Elgindy, 2025. "Numerical Solutions of Fractional Weakly Singular Two-Dimensional Partial Volterra Integral Equations Using Euler Wavelets," Mathematics, MDPI, vol. 13(17), pages 1-16, August.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:17:p:2718-:d:1731154
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/17/2718/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/17/2718/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:13:y:2025:i:17:p:2718-:d:1731154. 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: 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.