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Impulsive Delayed Lasota–Wazewska Fractional Models: Global Stability of Integral Manifolds

Author

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  • Gani Stamov

    (Department of Mathematics, Technical University of Sofia, 8800 Sliven, Bulgaria
    Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
    Current address: Affiliation 2.)

  • Ivanka Stamova

    (Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA)

Abstract

In this paper we deal with the problems of existence, boundedness and global stability of integral manifolds for impulsive Lasota–Wazewska equations of fractional order with time-varying delays and variable impulsive perturbations. The main results are obtained by employing the fractional Lyapunov method and comparison principle for impulsive fractional differential equations. With this research we generalize and improve some existing results on fractional-order models of cell production systems. These models and applied technique can be used in the investigation of integral manifolds in a wide range of biological and chemical processes.

Suggested Citation

  • Gani Stamov & Ivanka Stamova, 2019. "Impulsive Delayed Lasota–Wazewska Fractional Models: Global Stability of Integral Manifolds," Mathematics, MDPI, vol. 7(11), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1025-:d:282073
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    References listed on IDEAS

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    1. Hristo Kiskinov & Andrey Zahariev, 2015. "Nonlinear Impulsive Differential Equations with Weighted Exponential or Ordinary Dichotomous Linear Part in a Banach Space," International Journal of Differential Equations, Hindawi, vol. 2015, pages 1-7, September.
    2. 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.
    3. Škovránek, Tomáš & Podlubny, Igor & Petráš, Ivo, 2012. "Modeling of the national economies in state-space: A fractional calculus approach," Economic Modelling, Elsevier, vol. 29(4), pages 1322-1327.
    4. Li, Xiaodi & Yang, Xueyan & Huang, Tingwen, 2019. "Persistence of delayed cooperative models: Impulsive control method," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 130-146.
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