Fractional differential equations have been of great interest recently. This is because of both the intensive development of the theory of fractional calculus itself and the applications of such constructions in various scientific fields such as physics, mechanics, chemistry, engineering, etc. Differential equations with impulsive effects arising from the real world describe the dyn...

This paper is concerned with the existence of mild solutions for impulsive integro-differential equations with nonlocal conditions. We apply the technique measure of noncompactness in the space of piecewise continuous functions and by using Darbo-Sadovskii's fixed point theorem, we prove reasults about impulsive integro-differential equations for convex-power condensing operators.

In this paper we introduce some stability criteria for impulsive fuzzy system of differential equations with finite delay in states. Firstly, a new comparison principle for fuzzy differential system compared to crisp ordinary differential equation, based on a notion of upper quasi-monotone nondecreasing, in N dimentional state space is presented. Furthermore, in order to analyze the stability o...

Due to the plentiful dynamical behaviors, integro-differential equations with delays have many applications in a variety of fields such as control theory, biology, ecology, medicine, etc [1, 2]. Especially, the effects of delays on the stability of integro-differential equations have been extensively studied in the previous literature (see [3]-[9] and references cited therein). Besides delays, ...

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 prove the existence and uniqueness of solution to the impulsive fuzzy functional differential equations under generalized Hukuhara differentiability via the principle of contraction mappings. Some examples are provided to illustrate the result.

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...

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...

As the impulsive differential equations are useful in modelling many real processes observed in physics, chemistry, biology, engineering, etc., see [1, 11, 13, 20, 21, 22, 25, 26, 27], there has been an increasing interest in studying such equations from the point of view of stability, asymptotic behavior, existence of periodic solutions, and oscillation of solutions. The classical theory can b...