IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v153y2021ip1s0960077921008444.html
   My bibliography  Save this article

Explicit solutions and asymptotic behaviors of Caputo discrete fractional-order equations with variable coefficients

Author

Listed:
  • Du, Feifei
  • Lu, Jun-Guo

Abstract

A new discrete fractional-order Peano-Baker series is established in this paper. Based on this series, the explicit solutions of Caputo linear discrete fractional-order equations (DFOEs) with variable matrix coefficients involving the homogeneous and inhomogeneous cases are obtained. On the basis of the comparison theorem and the explicit solutions of Caputo linear DFOEs with variable coefficients, the asymptotic behaviors of the solutions of the homogeneous and inhomogeneous Caputo linear DFOEs with variable coefficients are presented. Finally, the applicability and effectiveness of the proposed results are illustrated by four examples.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p1:s0960077921008444
    DOI: 10.1016/j.chaos.2021.111490
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921008444
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111490?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. Restrepo, Joel E. & Ruzhansky, Michael & Suragan, Durvudkhan, 2021. "Explicit solutions for linear variable–coefficient fractional differential equations with respect to functions," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    2. 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).
    3. Yuan, Xiaolin & Mo, Lipo & Yu, Yongguang & Ren, Guojian, 2021. "Containment control of fractional discrete-time multi-agent systems with nonconvex constraints," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    4. 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).
    5. Wang, Jian & Zhu, Yuanguo & Gu, Yajing & Lu, Ziqiang, 2021. "Solutions of linear uncertain fractional order neutral differential equations," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    6. 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).
    7. 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).
    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. Wei, Yiheng & Su, Nan & Zhao, Linlin & Cao, Jinde, 2023. "LMI based stability condition for delta fractional order system with sector approximation," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

    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. 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).
    3. 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).
    4. 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).
    5. 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).
    6. Yang, Zhanying & Zhang, Jie & Zhang, Zhihui & Mei, Jun, 2023. "An improved criterion on finite-time stability for fractional-order fuzzy cellular neural networks involving leakage and discrete delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 910-925.
    7. Fernandez, Arran & Restrepo, Joel E. & Suragan, Durvudkhan, 2022. "On linear fractional differential equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    8. 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).
    9. 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.
    10. 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).
    11. 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).
    12. 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).
    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. Simon, S. Gimnitz & Bira, B. & Zeidan, Dia, 2023. "Optimal systems, series solutions and conservation laws for a time fractional cancer tumor model," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    15. Oscar Martínez-Fuentes & Fidel Meléndez-Vázquez & Guillermo Fernández-Anaya & José Francisco Gómez-Aguilar, 2021. "Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities," Mathematics, MDPI, vol. 9(17), pages 1-29, August.
    16. 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).
    17. Restrepo, Joel E. & Suragan, Durvudkhan, 2021. "Hilfer-type fractional differential equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    18. 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.
    19. Irgashev, B.Yu., 2023. "Initial boundary value problem for a high-order equation with two lines of degeneracy with the Caputo derivative," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    20. Zaky, M.A. & Hendy, A.S. & Suragan, D., 2022. "A note on a class of Caputo fractional differential equations with respect to another function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 289-295.

    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:153:y:2021:i:p1:s0960077921008444. 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.