Modelling and almost periodic processes in impulsive Lasota-Wazewska equations of fractional order with time-varying delays

Abstract

In this paper we propose an impulsive Caputo fractional-order Lasota-Wazewska model with time-varying delays. Applying the new fractional Lyapunov method we give  sufficient conditions for the existence of almost periodic solutions. The stability behavior of such solutions is also investigated. With this research we extend the theory of almost periodic solutions for impulsive Lasota-Wazewska models with delays to the fractional-order case. These models correspond basically to the survival of red blood cells: however, other applications are possible. Therefore, the applied technique can be used in the investigation of almost periodic processes in a wide range of possible models of cell production systems of diverse interest.

Mathematics Subject Classication (2010): 34K60, 34K14, 34K37, 34K45.

Key words: Lasota-Wazewska model, almost periodic solutions; fractional derivatives,
time-varying delays, impulsive perturbations.