IDEAS home Printed from https://ideas.repec.org/a/wsi/ijmpcx/v36y2025i01ns0129183124501766.html
   My bibliography  Save this article

A novel fixed point iteration process applied in solving the Caputo type fractional differential equations in Banach spaces

Author

Listed:
  • Godwin Amechi Okeke

    (Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, P.M.B. 1526, Owerri, Imo State, Nigeria)

  • Cyril Ifeanyichukwu Ugwuogor

    (Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri, P.M.B. 1526, Owerri, Imo State, Nigeria)

  • Rubayyi T. Alqahtani

    (��,§Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia)

  • Melike Kaplan

    (��Department of Computer Engineering, Faculty of Engineering and Architecture, Kastamonu University, Kastamonu, Türkiye)

  • W. Eltayeb Ahmed

    (��,§Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia)

Abstract

We introduce the modified Picard–Ishikawa hybrid iterative scheme and establish some strong convergence results for the class of asymptotically generalized ϕ-pseudocontractive mappings in the intermediate sense in Banach spaces and approximate the fixed point of this class of mappings via the newly introduced iteration scheme. We construct some numerical examples to support our results. Furthermore, we apply the Picard–Ishikawa hybrid iteration scheme in solving the nonlinear Caputo type fractional differential equations. Our results generalize, extend and unify several existing results in literature.

Suggested Citation

  • Godwin Amechi Okeke & Cyril Ifeanyichukwu Ugwuogor & Rubayyi T. Alqahtani & Melike Kaplan & W. Eltayeb Ahmed, 2025. "A novel fixed point iteration process applied in solving the Caputo type fractional differential equations in Banach spaces," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-19, January.
    • Handle: RePEc:wsi:ijmpcx:v:36:y:2025:i:01:n:s0129183124501766
    DOI: 10.1142/S0129183124501766
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0129183124501766
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0129183124501766?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:ijmpcx:v:36:y:2025:i:01:n:s0129183124501766. 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: http://www.worldscinet.com/ijmpc/ijmpc.shtml .

    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.