IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v158y2022ics0960077922002065.html
   My bibliography  Save this article

Some results on finite-time stability of stochastic fractional-order delay differential equations

Author

Listed:
  • Luo, Danfeng
  • Tian, Mengquan
  • Zhu, Quanxin

Abstract

Finite-time stability of stochastic fractional-order delay differential equations is researched here. Firstly, we derive the equivalent form of the considered system by using the Laplace transformation and its inverse. Subsequently, by defining the maximum weighted norm in Banach space and using the principle of contraction mapping, we prove that the solution of researched system is unique. What's more, by virtue of Henry-Grönwall delay inequality and interval translation, we derive the criterion of finite-time stability for the system with and without impulses, respectively. Finally, as a verification, examples are provided to expound the correctness of the deduced results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922002065
    DOI: 10.1016/j.chaos.2022.111996
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922002065
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.111996?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. Li, Mengmeng & Wang, JinRong, 2018. "Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 254-265.
    2. Du, Feifei & Lu, Jun-Guo, 2021. "New criterion for finite-time synchronization of fractional order memristor-based neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    3. 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).
    4. Danfeng Luo & Zhiguo Luo, 2018. "Uniqueness and Novel Finite-Time Stability of Solutions for a Class of Nonlinear Fractional Delay Difference Systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-7, September.
    5. Qien Li & Danfeng Luo & Zhiguo Luo & Quanxin Zhu, 2019. "On the Novel Finite-Time Stability Results for Uncertain Fractional Delay Differential Equations Involving Noninstantaneous Impulses," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-9, September.
    6. Du, Feifei & Lu, Jun-Guo, 2020. "Finite-time stability of neutral fractional order time delay systems with Lipschitz nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    7. 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.
    8. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Moualkia, Seyfeddine, 2023. "Mathematical analysis of new variant Omicron model driven by Lévy noise and with variable-order fractional derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Liu, Zhiguang & Zhu, Quanxin, 2023. "Ultimate boundedness of impulsive stochastic delay differential equations with delayed impulses," Statistics & Probability Letters, Elsevier, vol. 199(C).
    3. Dhayal, Rajesh & Zhu, Quanxin, 2023. "Stability and controllability results of ψ-Hilfer fractional integro-differential systems under the influence of impulses," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    4. Rhaima, Mohamed, 2023. "Ulam–Hyers stability for an impulsive Caputo–Hadamard fractional neutral stochastic differential equations with infinite delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 281-295.
    5. Amir Rezaie & Saleh Mobayen & Mohammad Reza Ghaemi & Afef Fekih & Anton Zhilenkov, 2023. "Design of a Fixed-Time Stabilizer for Uncertain Chaotic Systems Subject to External Disturbances," Mathematics, MDPI, vol. 11(15), pages 1-14, July.
    6. Huang, Jizhao & Luo, Danfeng & Zhu, Quanxin, 2023. "Relatively exact controllability for fractional stochastic delay differential equations of order κ∈(1,2]," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    7. Zhang, Yuan & Cao, Jinde & Liu, Lixia & Liu, Haihong & Li, Zhouhong, 2024. "Complex role of time delay in dynamical coordination of neural progenitor fate decisions mediated by Notch pathway," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    8. Jiang, Ziling & Huang, Fan & Shao, Haijian & Cai, Shuiming & Lu, Xiaobo & Jiang, Shengqin, 2023. "Time-varying finite-time synchronization analysis of attack-induced uncertain neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

    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. Chen, Yuting & Li, Xiaoyan & Liu, Song, 2021. "Finite-time stability of ABC type fractional delay difference equations," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Zhang, Zhe & Wang, Yaonan & Zhang, Jing & Ai, Zhaoyang & Liu, Feng, 2022. "Novel stability results of multivariable fractional-order system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Du, Feifei & Lu, Jun-Guo, 2021. "New approach to finite-time stability for fractional-order BAM neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    4. Du, Feifei & Lu, Jun-Guo, 2021. "Explicit solutions and asymptotic behaviors of Caputo discrete fractional-order equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    5. 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).
    6. Liu, Xiang & Wang, Peiguang & Anderson, Douglas R., 2022. "On stability and feedback control of discrete fractional order singular systems with multiple time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    7. Zhen Yang & Zhengqiu Zhang, 2022. "Finite-Time Synchronization Analysis for BAM Neural Networks with Time-Varying Delays by Applying the Maximum-Value Approach with New Inequalities," Mathematics, MDPI, vol. 10(5), pages 1-16, March.
    8. Zhang, Shaohua & Wang, Cong & Zhang, Hongli & Ma, Ping & Li, Xinkai, 2022. "Dynamic analysis and bursting oscillation control of fractional-order permanent magnet synchronous motor system," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    9. Christopher N. Angstmann & Stuart-James M. Burney & Bruce I. Henry & Byron A. Jacobs & Zhuang Xu, 2023. "A Systematic Approach to Delay Functions," Mathematics, MDPI, vol. 11(21), pages 1-34, November.
    10. Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Romero-Ugalde, H.M., 2019. "A novel method to solve variable-order fractional delay differential equations based in lagrange interpolations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 266-282.
    11. Sathiyaraj, T. & Fečkan, Michal & Wang, JinRong, 2020. "Null controllability results for stochastic delay systems with delayed perturbation of matrices," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    12. Hristo Kiskinov & Mariyan Milev & Andrey Zahariev, 2022. "About the Resolvent Kernel of Neutral Linear Fractional System with Distributed Delays," Mathematics, MDPI, vol. 10(23), pages 1-17, December.
    13. He, Jin-Man & Pei, Li-Jun, 2023. "Function matrix projection synchronization for the multi-time delayed fractional order memristor-based neural networks with parameter uncertainty," Applied Mathematics and Computation, Elsevier, vol. 454(C).
    14. Aydin, Mustafa & Mahmudov, Nazim I., 2022. "On a study for the neutral Caputo fractional multi-delayed differential equations with noncommutative coefficient matrices," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    15. Du, Feifei & Jia, Baoguo, 2020. "Finite time stability of fractional delay difference systems: A discrete delayed Mittag-Leffler matrix function approach," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    16. Wang, Mei & Du, Feifei & Chen, Churong & Jia, Baoguo, 2019. "Asymptotic stability of (q, h)-fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 158-167.
    17. Cui, Qian & Li, Lulu & Lu, Jianquan & Alofi, Abdulaziz, 2022. "Finite-time synchronization of complex dynamical networks under delayed impulsive effects," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    18. Lu, Qiu & Xiao, Min & Tao, Binbin & Huang, Chengdai & Shi, Shuo & Wang, Zhengxin & Jiang, Guoping, 2019. "Complex dynamic behaviors of a congestion control system under a novel PD1n control law: Stability, bifurcation and periodic oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 242-252.
    19. Shuang Wang & Hai Zhang & Weiwei Zhang & Hongmei Zhang, 2021. "Finite-Time Projective Synchronization of Caputo Type Fractional Complex-Valued Delayed Neural Networks," Mathematics, MDPI, vol. 9(12), pages 1-14, June.
    20. Ahmed M. Elshenhab & Xingtao Wang & Omar Bazighifan & Jan Awrejcewicz, 2022. "Finite-Time Stability Analysis of Linear Differential Systems with Pure Delay," Mathematics, MDPI, vol. 10(9), pages 1-10, April.

    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:chsofr:v:158:y:2022:i:c:s0960077922002065. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.