IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i8p1145-d1373480.html
   My bibliography  Save this article

Existence and Hyers–Ulam Stability for Random Impulsive Stochastic Pantograph Equations with the Caputo Fractional Derivative

Author

Listed:
  • Dongdong Gao

    (Department of Mathematics and Computer Science, Tongling University, Tongling 244000, China)

  • Jianli Li

    (College of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China)

Abstract

In this paper, we study the existence, uniqueness and Hyers–Ulam stability of a class of fractional stochastic pantograph equations with random impulses. Firstly, we establish sufficient conditions to ensure the existence of solutions for the considered equations by applying Schaefer’s fixed point theorem under relaxed linear growth conditions. Secondly, we prove the solution for the considered equations is Hyers–Ulam stable via Gronwall’s inequality. Moreover, the previous literature will be significantly generalized in our paper. Finally, an example is given to explain the efficiency of the obtained results.

Suggested Citation

  • Dongdong Gao & Jianli Li, 2024. "Existence and Hyers–Ulam Stability for Random Impulsive Stochastic Pantograph Equations with the Caputo Fractional Derivative," Mathematics, MDPI, vol. 12(8), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:8:p:1145-:d:1373480
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/8/1145/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/8/1145/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mao, Wei & Hu, Liangjian & Mao, Xuerong, 2015. "The existence and asymptotic estimations of solutions to stochastic pantograph equations with diffusion and Lévy jumps," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 883-896.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wan, Fangzhe & Hu, Po & Chen, Huabin, 2020. "Stability analysis of neutral stochastic differential delay equations driven by Lévy noises," Applied Mathematics and Computation, Elsevier, vol. 375(C).

    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:12:y:2024:i:8:p:1145-:d:1373480. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.