Existence and controllability of second-order neutral impulsive stochastic evolution integro-differential equations with state-dependent delay

On Controllability of Impulsive Fractional Integro-differential Nonlocal System with State

“…Aimene et al [18] used the Drabo fixed point theorem and the properties of measures of noncompactness with semigroup theory to obtain the controllability of impulsive fractional differential equations with delay. Huang et al [33] derived a set of sufficient conditions for the existence and controllability of mild solutions for a class of second-order neutral impulsive stochastic evolution integro-differential equations with statedependent delay by using fixed point theorems. MA and LIU [17] discussed the exact controllability of fractional neutral integro-differential equations with state-dependent delay in Banach spaces with the help of fixed point theorems and fractional calculus.…”

Approximate Controllability of Non-Instantaneous Impulsive Stochastic Evolution Systems Driven by Fractional Brownian Motion with Hurst Parameter H∈(0,12)

“…On the other side, impulsive dynamical systems arise in the description of mathematical modeling of real-world systems which are affected by instantaneous perturbations or non-instantaneous impulses (see, for example, [10][11][12][13][14][15][16] and the references therein). Naturally, the controllability of impulsive stochastic differential equations (ISDEs) have been discussed heatedly; for example, see [17][18][19][20][21][22] and the references therein. In the case of non-instantaneous impulses, for instance, the approximate controllability of a class of multi-valued impulsive fractional stochastic partial integro-differential equation (FISPIDE) with infinite delay was explored by Yan and Lu [23]; recently, Yan and Han [24] derived the approximate controllability result of a type of neutral FISPIDE with noncompact operators.…”

Approximate controllability of retarded impulsive stochastic integro-differential equations driven by fractional Brownian motion

“…The impulsive neutral integro-differential equations with delay properties has been used for modeling the evolution of physical systems, in which the response of the system depends not only on the current state, but also on the past history of the system. Several authors have investigated the impulsive neutral integrodifferential equations with delay (see [19,20,28,35,43]) and references therein.…”