The aim of this paper is to use the Reproducing kernel Hilbert Space Method (RKHSM) to solve the linear and nonlinear fuzzy impulsive fractional differential equations. Finding the numerical solutionsof this class of equations are a difficult topic to analyze. In this study, convergence analysis, estimations error and bounds errors are discussed in detail under some hypotheses which provi...

In this paper, a class of impulsive functional differential systems is investigated. It is proved that for the asymptotic stability of the zero solution of the system considered, it is sufficient that only some components of the right-hand side of the system are bounded for unbounded values of time. For functional differential equations without impulses, similar results were proved by Burton an...

Impulsive differential equations are a basic tool for studying evolution processes of real life phenomena that are subjected to sudden changes at certain instants. In view of multiple applications of the impulsive differential equations, it is necessary to develop the methods for their solvability. Unfortunately, a comparatively small class of impulsive differential equations can be solved anal...

Abstract: The current paper is concerned with the controllability of nonlocal secondorder impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a ne...

We define two models of hysteresis that generalize the Preisach model. The first model is deterministic, the second model is stochastic and it utilizes discontinuous transition probabilities that satisfy impulsive differential equations. For the first model we prove, among other things, a local version of the "wiping out" property; for the stochastic model, we give methods for the construction ...

Abstract. In this paper we discuss the existence of PC-mild solutions for Cauchy problems and nonlocal problems for impulsive fractional evolution equations involving Caputo fractional derivative. By utilizing the theory of operators semigroup, probability density functions via impulsive conditions, a new concept on a PC-mild solution for our problem is introduced. Our main techniques based on ...

It is characteristic for a linear ordinary differential equation that if any solution is bounded on the half-line for any bounded right-hand side then a solution of the corresponding homogeneous equation tends to zero exponentially [1]. The connection of boundedness with exponential behavior of solutions for impulsive differential equations is studied in [2,3] and many other papers. It turns ou...