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

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.

An investigation on the Lasota-Wazewska model with a piecewise constant argument

“…Further, we refer to [34] for biological models, involving chemotaxis and nonlinear diffusive mechanism, formulated by the introduction of reactions coupling growth and death impacts. The well known Lasota-Wazewska model (1.2) was extended and generalized by many authors, see for example [3,19,22,23,29,30,32,33,43,65] including some recent publications on the topic [8,11,14,26,52,54,56,64].…”

Impulsive Fractional Differential Inclusions and Almost Periodic Waves

“…Due to the great possibilities in terms of their applications, impulsive perturbations have been considered for fractional-order differential systems, and the theory of impulsive fractional differential systems has been also very well-studied. We will mention several publications that give basic results for such systems [31][32][33][34][35][36][37].…”

Fractional Lotka-Volterra-Type Cooperation Models: Impulsive Control on Their Stability Behavior

“…In addition, the extended impulsive fractional-order case has also attracted the attention of many researchers [ 38 , 39 , 40 ]. Impulsive effects in fractional biological models are considered by several authors [ 38 , 39 , 41 , 42 , 43 ], including some fractional Lotka-Volterra models [ 39 , 44 ]. However, most of the studies considered competitive models, and to the best of our knowledge, there are no results on fractional cooperative models.…”