A class of nonlinear non-instantaneous impulsive differential equations involving parameters and fractional order

In this article, we study asymptotic and smooth properties of solutions to nonlinear non-instantaneous impulsive differential equations involving parameters of integer order and fractional order. We introduce the concept of continuous dependence and differentiability of solutions and establish sufficient conditions to guarantee the solution depends continuously and is differentiable on the initial condition, impulsive parameters and junction parameters. Finally, two models of non-instantaneous impulsive logistic equations are given to illustrate our results.