Asymptotic properties of the solutions of nonlinear non-instantaneous impulsive differential equations

Abstract

In this article, we investigate asymptotic properties of solutions, continuous dependence and stability, of integer order and fractional order nonlinear non-instantaneous impulsive differential equations (IDEs). We introduce the concept of continuous dependence and stability of solutions to integer order and fractional order non-instantaneous impulsive Cauchy problems (ICPs) and establish sufficient conditions to guarantee that the solutions of both the original and the perturbed non-instantaneous ICPs are close to each other in a certain sense. Finally, examples are given to illustrate our results.