Asymptotical stability and asymptotic periodicity for the Lasota-Wazewska model of fractional order with infinite delays

In this paper, we study a class of nonlinear fractional-order Lasota-Wazewska model with infinite delays. Firstly, we introduce some definitions, lemmas of fraction-order differential equation and a number of properties of Mittag-Le er function. Then, based on these prepared knowledge and by applying the comparison theorem of fractional-order differential equation and the relationship between characteristic equation of Laplace transform and stability, we prove the permanence, asymptotic stability and asymptotic periodicity of fractional-order Lasota-Wazewska model. After that, we introduce an example to illustrate the main results.