IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v190y2021icp429-448.html
   My bibliography  Save this article

Strong convergence of a Euler–Maruyama method for fractional stochastic Langevin equations

Author

Listed:
  • Ahmadova, Arzu
  • Mahmudov, Nazim I.

Abstract

The novelty of this paper is to derive a mild solution by means of recently defined Mittag-Leffler type functions of fractional stochastic Langevin equations of orders α∈(1,2] and β∈(0,1] whose coefficients satisfy standard Lipschitz and linear growth conditions. Then, we prove existence and uniqueness results of mild solution and show the coincidence between the notion of mild solution and integral equation. For this class of system, we construct fractional Euler–Maruyama method and establish new results on strong convergence of this method for fractional stochastic Langevin equations. We also introduce a general form of the nonlinear fractional stochastic Langevin equation and derive a general mild solution. Finally, the numerical examples are illustrated to verify the main theory.

Suggested Citation

  • Ahmadova, Arzu & Mahmudov, Nazim I., 2021. "Strong convergence of a Euler–Maruyama method for fractional stochastic Langevin equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 429-448.
    • Handle: RePEc:eee:matcom:v:190:y:2021:i:c:p:429-448
    DOI: 10.1016/j.matcom.2021.05.037
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475421002226
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2021.05.037?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. Zhang, Tong & Li, ShiShun, 2017. "A posteriori error estimates of finite element method for the time-dependent Navier–Stokes equations," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 13-26.
    2. 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).
    3. Pedjeu, Jean-C. & Ladde, Gangaram S., 2012. "Stochastic fractional differential equations: Modeling, method and analysis," Chaos, Solitons & Fractals, Elsevier, vol. 45(3), pages 279-293.
    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. Abdelhamid Mohammed Djaouti & Zareen A. Khan & Muhammad Imran Liaqat & Ashraf Al-Quran, 2024. "Existence, Uniqueness, and Averaging Principle of Fractional Neutral Stochastic Differential Equations in the L p Space with the Framework of the Ψ-Caputo Derivative," Mathematics, MDPI, vol. 12(7), pages 1-21, March.
    2. 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).
    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. Huseynov, Ismail T. & Ahmadova, Arzu & Fernandez, Arran & Mahmudov, Nazim I., 2021. "Explicit analytical solutions of incommensurate fractional differential equation systems," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    5. Abouagwa, Mahmoud & Liu, Jicheng & Li, Ji, 2018. "Carathéodory approximations and stability of solutions to non-Lipschitz stochastic fractional differential equations of Itô-Doob type," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 143-153.
    6. Hendy, Ahmed S. & Zaky, Mahmoud A. & Suragan, Durvudkhan, 2022. "Discrete fractional stochastic Grönwall inequalities arising in the numerical analysis of multi-term fractional order stochastic differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 269-279.
    7. Abdellatif Ben Makhlouf & Lassaad Mchiri & Hakeem A. Othman & Hafedh M. S. Rguigui & Salah Boulaaras, 2023. "Proportional Itô–Doob Stochastic Fractional Order Systems," Mathematics, MDPI, vol. 11(9), pages 1-14, April.
    8. Linna Liu & Feiqi Deng & Boyang Qu & Yanhong Meng, 2022. "Fundamental Properties of Nonlinear Stochastic Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-18, July.
    9. Seyfeddine Moualkia & Yong Xu, 2021. "On the Existence and Uniqueness of Solutions for Multidimensional Fractional Stochastic Differential Equations with Variable Order," Mathematics, MDPI, vol. 9(17), pages 1-12, August.
    10. Ahmadova, Arzu & Mahmudov, Nazim I., 2021. "Ulam–Hyers stability of Caputo type fractional stochastic neutral differential equations," Statistics & Probability Letters, Elsevier, vol. 168(C).
    11. Zakaria Ali & Minyahil Abera Abebe & Talat Nazir, 2024. "Strong Convergence of Euler-Type Methods for Nonlinear Fractional Stochastic Differential Equations without Singular Kernel," Mathematics, MDPI, vol. 12(18), pages 1-36, September.
    12. Yang, Zhiwei & Zheng, Xiangcheng & Zhang, Zhongqiang & Wang, Hong, 2021. "Strong convergence of a Euler-Maruyama scheme to a variable-order fractional stochastic differential equation driven by a multiplicative white noise," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    13. Upadhyay, Anjali & Kumar, Surendra, 2023. "The exponential nature and solvability of stochastic multi-term fractional differential inclusions with Clarke’s subdifferential," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    14. Kahouli, Omar & Ben Makhlouf, Abdellatif & Mchiri, Lassaad & Rguigui, Hafedh, 2023. "Hyers–Ulam stability for a class of Hadamard fractional Itô–Doob stochastic integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 166(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:eee:matcom:v:190:y:2021:i:c:p:429-448. 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.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.