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

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  • 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
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    References listed on IDEAS

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    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
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    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).

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