IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i7p1013-d776672.html
   My bibliography  Save this article

Existence and Hyers–Ulam Stability for a Multi-Term Fractional Differential Equation with Infinite Delay

Author

Listed:
  • Chen Chen

    (School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China)

  • Qixiang Dong

    (School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China)

Abstract

This paper is devoted to investigating one type of nonlinear two-term fractional order delayed differential equations involving Caputo fractional derivatives. The Leray–Schauder alternative fixed-point theorem and Banach contraction principle are applied to analyze the existence and uniqueness of solutions to the problem with infinite delay. Additionally, the Hyers–Ulam stability of fractional differential equations is considered for the delay conditions.

Suggested Citation

  • Chen Chen & Qixiang Dong, 2022. "Existence and Hyers–Ulam Stability for a Multi-Term Fractional Differential Equation with Infinite Delay," Mathematics, MDPI, vol. 10(7), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1013-:d:776672
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/7/1013/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/7/1013/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. D. Baleanu & S. J. Sadati & R. Ghaderi & A. Ranjbar & T. Abdeljawad (Maraaba) & F. Jarad, 2010. "Razumikhin Stability Theorem for Fractional Systems with Delay," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-9, June.
    2. Chen, Boshan & Chen, Jiejie, 2015. "Razumikhin-type stability theorems for functional fractional-order differential systems and applications," Applied Mathematics and Computation, Elsevier, vol. 254(C), pages 63-69.
    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. Huizhen Qu & Jianwen Zhou & Tianwei Zhang, 2022. "Three-Point Boundary Value Problems of Coupled Nonlocal Laplacian Equations," Mathematics, MDPI, vol. 10(13), pages 1-18, June.

    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. Ravi Agarwal & Snezhana Hristova & Donal O’Regan, 2022. "Generalized Proportional Caputo Fractional Differential Equations with Delay and Practical Stability by the Razumikhin Method," Mathematics, MDPI, vol. 10(11), pages 1-15, May.
    2. Ravi Agarwal & Snezhana Hristova & Donal O’Regan, 2021. "Stability Concepts of Riemann-Liouville Fractional-Order Delay Nonlinear Systems," Mathematics, MDPI, vol. 9(4), pages 1-16, February.
    3. Yao, Xueqi & Zhong, Shouming, 2021. "EID-based robust stabilization for delayed fractional-order nonlinear uncertain system with application in memristive neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    4. Aghayan, Zahra Sadat & Alfi, Alireza & Mousavi, Yashar & Kucukdemiral, Ibrahim Beklan & Fekih, Afef, 2022. "Guaranteed cost robust output feedback control design for fractional-order uncertain neutral delay systems," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    5. Zhang, Lingzhong & Yang, Yongqing & Wang, Fei, 2017. "Projective synchronization of fractional-order memristive neural networks with switching jumps mismatch," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 402-415.
    6. Chen, Shenglong & Yang, Jikai & Li, Zhiming & Li, Hong-Li & Hu, Cheng, 2023. "New results for dynamical analysis of fractional-order gene regulatory networks with time delay and uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    7. Ning, Jinghua & Hua, Changchun, 2022. "H∞ output feedback control for fractional-order T-S fuzzy model with time-delay," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    8. Yang, Zhanwen & Li, Qi & Yao, Zichen, 2023. "A stability analysis for multi-term fractional delay differential equations with higher order," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    9. Fei Qi & Yi Chai & Liping Chen & José A. Tenreiro Machado, 2020. "Delay-Dependent and Order-Dependent Guaranteed Cost Control for Uncertain Fractional-Order Delayed Linear Systems," Mathematics, MDPI, vol. 9(1), pages 1-13, December.
    10. Sakthivel, R. & Sweetha, S. & Tatar, N.E. & Panneerselvam, V., 2023. "Delayed reset control design for uncertain fractional-order systems with actuator faults via dynamic output feedback scheme," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    11. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun, 2017. "Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 416-422.
    12. Peng, Qiu & Jian, Jigui, 2023. "Asymptotic synchronization of second-fractional -order fuzzy neural networks with impulsive effects," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    13. Yan, Hongyun & Qiao, Yuanhua & Duan, Lijuan & Miao, Jun, 2022. "New results of quasi-projective synchronization for fractional-order complex-valued neural networks with leakage and discrete delays," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    14. Thabet Abdeljawad & Fadila Madjidi & Fahd Jarad & Ndolane Sene, 2019. "On Dynamic Systems in the Frame of Singular Function Dependent Kernel Fractional Derivatives," Mathematics, MDPI, vol. 7(10), pages 1-13, October.
    15. Li, Hong-Li & Jiang, Yao-Lin & Wang, Zuolei & Zhang, Long & Teng, Zhidong, 2015. "Global Mittag–Leffler stability of coupled system of fractional-order differential equations on network," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 269-277.
    16. Wang, Fei & Zheng, Zhaowen & Yang, Yongqing, 2021. "Quasi-synchronization of heterogenous fractional-order dynamical networks with time-varying delay via distributed impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    17. Chen, Juan & Zhou, Hua-Cheng & Zhuang, Bo & Xu, Ming-Hua, 2023. "Active disturbance rejection control to stabilization of coupled delayed time fractional-order reaction–advection–diffusion systems with boundary disturbances and spatially varying coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    18. Shafiya, M. & Nagamani, G. & Dafik, D., 2022. "Global synchronization of uncertain fractional-order BAM neural networks with time delay via improved fractional-order integral inequality," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 168-186.
    19. Yao, Zichen & Yang, Zhanwen & Zhang, Yusong, 2021. "A stability criterion for fractional-order complex-valued differential equations with distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    20. Chen, Liping & Li, Xiaomin & Chen, YangQuan & Wu, Ranchao & Lopes, António M. & Ge, Suoliang, 2022. "Leader-follower non-fragile consensus of delayed fractional-order nonlinear multi-agent systems," Applied Mathematics and Computation, Elsevier, vol. 414(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:10:y:2022:i:7:p:1013-:d:776672. 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.