IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v195y2023ics0167715222002814.html
   My bibliography  Save this article

Well-posedness and regularity for solutions of Caputo stochastic fractional delay differential equations

Author

Listed:
  • Huong, P.T.
  • The, N.T.

Abstract

This paper is devoted to build the well-posedness and regularity for solutions of Caputo stochastic fractional delay differential equations (for short CSFDDE) of order α∈(12,1). Firstly, under local Lipschitz condition of coefficients, we show a result on the existence and uniqueness of solutions. Secondly, under global Lipschitz condition of coefficients, we show the continuous dependence of solutions on the initial values and on the fractional exponent α and the regularity in time for solutions is also derived. The main ingredient in the proof is to use a temporally weighted norm, Banach fixed point theorem and truncation procedure.

Suggested Citation

  • Huong, P.T. & The, N.T., 2023. "Well-posedness and regularity for solutions of Caputo stochastic fractional delay differential equations," Statistics & Probability Letters, Elsevier, vol. 195(C).
  • Handle: RePEc:eee:stapro:v:195:y:2023:i:c:s0167715222002814
    DOI: 10.1016/j.spl.2022.109768
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715222002814
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spl.2022.109768?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.

    References listed on IDEAS

    as
    1. Anh, P.T. & Doan, T.S. & Huong, P.T., 2019. "A variation of constant formula for Caputo fractional stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 351-358.
    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. Luo, Danfeng & Tian, Mengquan & Zhu, Quanxin, 2022. "Some results on finite-time stability of stochastic fractional-order delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. James Hoult & Yubin Yan, 2024. "Numerical Approximation for a Stochastic Fractional Differential Equation Driven by Integrated Multiplicative Noise," Mathematics, MDPI, vol. 12(3), pages 1-18, January.
    3. Xu, Shuli & Feng, Yuqiang & Jiang, Jun & Nie, Na, 2022. "A variation of constant formula for Caputo fractional stochastic differential equations with jump–diffusion," Statistics & Probability Letters, Elsevier, vol. 185(C).
    4. Lu, Ziqiang & Zhu, Yuanguo, 2022. "Nonlinear impulsive problems for uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    5. Ahmadova, Arzu & Mahmudov, Nazim I., 2020. "Existence and uniqueness results for a class of fractional stochastic neutral differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    6. Giacomo Ascione & Enrica Pirozzi, 2020. "On the Construction of Some Fractional Stochastic Gompertz Models," Mathematics, MDPI, vol. 8(1), pages 1-24, January.

    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:eee:stapro:v:195:y:2023:i:c:s0167715222002814. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.