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On Dynamic Systems in the Frame of Singular Function Dependent Kernel Fractional Derivatives
Open AccessArticle

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

by Gani Stamov 1,2,† and Ivanka Stamova 2,*
1
Department of Mathematics, Technical University of Sofia, 8800 Sliven, Bulgaria
2
Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
*
Author to whom correspondence should be addressed.
Current address: Affiliation 2.
Mathematics 2019, 7(11), 1025; https://doi.org/10.3390/math7111025
Received: 9 October 2019 / Revised: 24 October 2019 / Accepted: 26 October 2019 / Published: 31 October 2019
(This article belongs to the Special Issue Stability Analysis of Fractional Systems)
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. View Full-Text
Keywords: global stability; integral manifolds; impulsive Lasota–Wazewska models; functional derivatives; variable impulsive perturbations; time-varying delays global stability; integral manifolds; impulsive Lasota–Wazewska models; functional derivatives; variable impulsive perturbations; time-varying delays
MDPI and ACS Style

Stamov, G.; Stamova, I. Impulsive Delayed Lasota–Wazewska Fractional Models: Global Stability of Integral Manifolds. Mathematics 2019, 7, 1025.

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