IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v13y2025i8p1252-d1632219.html
   My bibliography  Save this article

Generalized Grönwall Inequality and Ulam–Hyers Stability in ℒ p Space for Fractional Stochastic Delay Integro-Differential Equations

Author

Listed:
  • Abdelhamid Mohammed Djaouti

    (Department of Mathematics and Statistics, Faculty of Sciences, King Faisal University, Al Hofuf 31982, Saudi Arabia)

  • Muhammad Imran Liaqat

    (Department of Mathematics, National College of Business Administration & Economics, Lahore 54000, Pakistan)

Abstract

In this work, we derive novel theoretical results concerning well-posedness and Ulam–Hyers stability. Specifically, we investigate the well-posedness of Caputo–Katugampola fractional stochastic delay integro-differential equations. Additionally, we develop a generalized Grönwall inequality and apply it to prove Ulam–Hyers stability in L p space. Our findings generalize existing results for fractional derivatives and space, as we formulate them in the Caputo–Katugampola fractional derivative and L p space. To support our theoretical results, we present an illustrative example.

Suggested Citation

  • Abdelhamid Mohammed Djaouti & Muhammad Imran Liaqat, 2025. "Generalized Grönwall Inequality and Ulam–Hyers Stability in ℒ p Space for Fractional Stochastic Delay Integro-Differential Equations," Mathematics, MDPI, vol. 13(8), pages 1-23, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1252-:d:1632219
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/13/8/1252/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/13/8/1252/
    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:2025:i:8:p:1252-:d:1632219. 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.