Impulsive differential equations, which arise in physics, population dynamics, economics, and so forth, are important mathematical tools for providing a better understanding of many real-world models, we refer to [1–5] and the references therein. About the applications of the theory of impulsive differential equations to different areas, for example, see [6–15]. Boundary value problems (BVPs) f...

In this paper, we proposed a method for computing the approximate solution for impulsive fuzzy differential equations by utilizing the existing results in impulsive differential equations and fuzzy differential equations. The numerical solutions are investigated since many impulsive differential equations cannot be solved analytically or their solving is complicated. The solutions are then comp...

Keywords: Fractional differential equations Impulsive fractional differential equations Impulse General solution Existence a b s t r a c t In this paper, for impulsive differential equations with fractional-order q 2 ð0; 1Þ, we show that the formula of solutions in cited papers are incorrect. Secondly, we find out a formula of the general solution for impulsive Cauchy problem with Caputo fracti...

In this paper, we study the problem of controllability of impulsive neutral evolution integrodifferential equations with state dependent delay in Banach spaces. The main results are completely new and are obtained by using Sadovskii’s fixed point theorem, theory of resolvent operators, and an abstract phase space. An example is given to illustrate the theory.

ABSTRACT. In order to describe various real-world problems in physical and engineering sciences that are subject to abrupt changes at certain instants during the evolution process, impulsive differential equations has been used to describe the system model. In this article, the problem of approximate controllability for nonlinear impulsive neutral differential inclusions with nonlocal condition...

*Correspondence: [email protected] 1Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, P.R. China Full list of author information is available at the end of the article Abstract By processing the problem through fixed point theory and propagator theory, we investigate the periodicity of solutions to a class of impulsive evolution equations in Hilbert spaces and estab...