This paper is mainly concerned with the existence of solutions of impulsive fractional neutral functional differential equations in Banach Spaces. The results are obtained by using Krasnoselskii’s fixed point theorem.

This paper studies the oscillation properties of higher order impulsive delay differential equations, and some sufficient conditions for all bounded solutions of this kind of higher order impulsive delay differential equations to be nonoscillatory are obtained by using a comparison theorem with corresponding nonimpulsive differential equations. AMS subject classification: 34C10, 34C15.

In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.

Impulsive differential equations, which arise in biology, physics, population dynamics, economics, and so forth, are a basic tool to study evolution processes that are subjected to abrupt in their states see 1–4 . Many literatures have been published about existence of solutions for first-order and second-order impulsive ordinary differential equations with boundary conditions 5–19 , which are ...

In this paper, we consider a class of nonlinear impulsive delay differential equations. By establishing an exponential estimate for delay differential inequality with impulsive initial condition and employing Banach fixed point theorem, we obtain several sufficient conditions ensuring the existence, uniqueness and global exponential stability of a periodic solution for nonlinear impulsive delay...

In this article we derive existence and comparison results for discontinuous non-absolute functional integral equations of Volterra type in an ordered Banach space which has a regular order cone. The obtained results are then applied to first-order impulsive differential equations.

* Correspondence: [email protected]. cn Department of Mathematics, Southeast University, Nanjing 210096, P. R. China Full list of author information is available at the end of the article Abstract In this article, by using Razumikhin-type technique, we investigate pth moment exponential stability of stochastic functional differential equations with Markovian switching and delayed impulses. Several ...

In 1991, the first paper on impulsive partial differential equations [1] was published. For an excellent exposition of this paper and its applications, see [2]. The oscillation theory of impulsive partial differential equations have wide applications in such subjects as control theory, meteorology, biology, medicine, engineering, chemistry and physics. Many results can be found [3-14]. However,...