IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v349y2019icp158-167.html
   My bibliography  Save this article

Asymptotic stability of (q, h)-fractional difference equations

Author

Listed:
  • Wang, Mei
  • Du, Feifei
  • Chen, Churong
  • Jia, Baoguo

Abstract

Asymptotic stability of linear nabla Riemann–Liouville (q, h)-fractional difference equation is investigated in this paper. A Liapunov functional is constructed for the fractional difference equation. The sufficient condition for the asymptotic stability of considered equations is proposed. The results are illustrated with the corresponding numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:158-167
    DOI: 10.1016/j.amc.2018.12.039
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318311007
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.12.039?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. Pinto, Carla M.A. & Carvalho, Ana R.M., 2017. "The role of synaptic transmission in a HIV model with memory," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 76-95.
    2. Zhihong Bai & Run Xu, 2018. "The Asymptotic Behavior of Solutions for a Class of Nonlinear Fractional Difference Equations with Damping Term," Discrete Dynamics in Nature and Society, Hindawi, vol. 2018, pages 1-11, January.
    3. 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.
    4. Jiqiang Jiang & Lishan Liu & Yonghong Wu, 2012. "Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-21, June.
    5. Zhang, Jun & Wang, JinRong, 2018. "Numerical analysis for Navier–Stokes equations with time fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 481-489.
    6. Jan Čermák & Tomáš Kisela & Luděk Nechvátal, 2011. "Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-21, June.
    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. Wang, Mei & Jia, Baoguo & Chen, Churong & Zhu, Xiaojuan & Du, Feifei, 2020. "Discrete fractional Bihari inequality and uniqueness theorem of solutions of nabla fractional difference equations with non-Lipschitz nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 376(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. Kui Liu & Michal Fečkan & D. O’Regan & JinRong Wang, 2019. "Hyers–Ulam Stability and Existence of Solutions for Differential Equations with Caputo–Fabrizio Fractional Derivative," Mathematics, MDPI, vol. 7(4), pages 1-14, April.
    2. 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).
    3. Xu, Changjin & Liao, Maoxin & Li, Peiluan & Guo, Ying & Xiao, Qimei & Yuan, Shuai, 2019. "Influence of multiple time delays on bifurcation of fractional-order neural networks," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 565-582.
    4. Jang, Bongsoo & Kim, Hyunju, 2024. "Mapping techniques for collocation method of time-fractional convection–diffusion equations in domains with cracks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 60-79.
    5. 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.
    6. 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.
    7. 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).
    8. 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.
    9. 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).
    10. 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).
    11. Wu, Guo-Cheng & Baleanu, Dumitru & Luo, Wei-Hua, 2017. "Lyapunov functions for Riemann–Liouville-like fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 228-236.
    12. Ahmed Salem & Rawia Babusail, 2022. "Finite-Time Stability in Nonhomogeneous Delay Differential Equations of Fractional Hilfer Type," Mathematics, MDPI, vol. 10(9), pages 1-14, May.
    13. 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.
    14. 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).
    15. Prakash, M. & Rakkiyappan, R. & Manivannan, A. & Cao, Jinde, 2019. "Dynamical analysis of antigen-driven T-cell infection model with multiple delays," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 266-281.
    16. 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.
    17. Ravi Agarwal & Snezhana Hristova & Donal O’Regan, 2019. "Explicit Solutions of Initial Value Problems for Linear Scalar Riemann-Liouville Fractional Differential Equations With a Constant Delay," Mathematics, MDPI, vol. 8(1), pages 1-14, December.
    18. Pang, Denghao & Jiang, Wei & Liu, Song & Jun, Du, 2019. "Stability analysis for a single degree of freedom fractional oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 498-506.
    19. Ekaterina Madamlieva & Hristo Kiskinov & Milena Petkova & Andrey Zahariev, 2022. "On the Preservation with Respect to Nonlinear Perturbations of the Stability Property for Nonautonomous Linear Neutral Fractional Systems with Distributed Delays," Mathematics, MDPI, vol. 10(15), pages 1-20, July.
    20. Zafar, Zain Ul Abadin & Ali, Nigar & Baleanu, Dumitru, 2021. "Dynamics and numerical investigations of a fractional-order model of toxoplasmosis in the population of human and cats," Chaos, Solitons & Fractals, Elsevier, vol. 151(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:apmaco:v:349:y:2019:i:c:p:158-167. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.