IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2024i1p33-d1553707.html
   My bibliography  Save this article

A Novel and Efficient Iterative Approach to Approximating Solutions of Fractional Differential Equations

Author

Listed:
  • Doaa Filali

    (Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Nidal H. E. Eljaneid

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

  • Adel Alatawi

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

  • Esmail Alshaban

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

  • Montaser Saudi Ali

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

  • Faizan Ahmad Khan

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

Abstract

This study presents a novel and efficient iterative approach to approximating the fixed points of contraction mappings in Banach spaces, specifically approximating the solutions of nonlinear fractional differential equations of the Caputo type. We establish two theorems proving the stability and convergence of the proposed method, supported by numerical examples and graphical comparisons, which indicate a faster convergence rate compared to existing methods, including those by Agarwal, Gursoy, Thakur, Ali and Ali, and D ∗ ∗ . Additionally, a data dependence result for approximate operators using the proposed method is provided. This approach is applied to achieve the solutions for Caputo-type fractional differential equations with boundary conditions, demonstrating the efficacy of the method in practical applications.

Suggested Citation

  • Doaa Filali & Nidal H. E. Eljaneid & Adel Alatawi & Esmail Alshaban & Montaser Saudi Ali & Faizan Ahmad Khan, 2024. "A Novel and Efficient Iterative Approach to Approximating Solutions of Fractional Differential Equations," Mathematics, MDPI, vol. 13(1), pages 1-18, December.
    • Handle: RePEc:gam:jmathe:v:13:y:2024:i:1:p:33-:d:1553707
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/1/33/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/1/33/
    Download Restriction: no
    ---><---

    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:2024:i:1:p:33-:d:1553707. 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.