IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v33y2025i04ns0218348x25400699.html
   My bibliography  Save this article

The Prospective Analysis Of Three-Dimensional Time-Fractional Helmholtz Model Using A New Iterative Method

Author

Listed:
  • MUHAMMAD NADEEM

    (School of Mathematics and Statistics, Qujing Normal University, Qujing 655011, P. R. China)

  • OMAR ABU ARQUB

    (��Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan)

  • LOREDANA FLORENTINA IAMBOR

    (��Department of Mathematics and Computer Science, University of Oradea, 1 University Street, 410087 Oradea, Romania)

  • MOHAMED HUSSIEN

    (�Department of Chemistry, Faculty of Science, King Khalid University, P. O. Box 9004, Abha 61413, Saudi Arabia)

  • EBRAHEEM ALZAHRANI

    (�Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia)

Abstract

This work proposes a new iterative method (NIM) for the analytical examination of a three-dimensional time fractional Helmholtz problem with the appropriate initial conditions that arise in various natural models. We examine the concept of fractional operators by the means of Caputo order. The Sumudu transform (ST) is coupled with the homotopy perturbation method (HPM) to develop the concept of NIM. We present two numerical examples of fractional order to demonstrate the effectiveness and validity of the proposed technique. This research presents the relationship between the NIM results and the actual outcomes for the 3D fractional Helmholtz model. The NIM results indicate that as the terms of the series solution increase, the solution progressively aligns with the actual solution. The computed values specifically demonstrate that the approach for addressing fractional order problems in physical models is extremely precise and simple to comprehend.

Suggested Citation

  • Muhammad Nadeem & Omar Abu Arqub & Loredana Florentina Iambor & Mohamed Hussien & Ebraheem Alzahrani, 2025. "The Prospective Analysis Of Three-Dimensional Time-Fractional Helmholtz Model Using A New Iterative Method," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(04), pages 1-12.
    • Handle: RePEc:wsi:fracta:v:33:y:2025:i:04:n:s0218348x25400699
    DOI: 10.1142/S0218348X25400699
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X25400699
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X25400699?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.

    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:wsi:fracta:v:33:y:2025:i:04:n:s0218348x25400699. 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.