Existence of solutions for a impulsive nonlocal stochastic functional integrodifferential inclusion in Hilbert spaces

On the initial value problem of fractional stochastic evolution equations in Hilbert spaces

“…However, we observed that most of the existing articles (see, for example [43][44][45][46][47][48][49]) are only devoted to investigating the local existence, uniqueness and controllability of mild solutions as well as the asymptotic stability for fractional stochastic evolution equations, up until now the existence of saturated mild solutions and global mild solutions and also the continuous dependence of mild solutions on parameters as well as the asymptotical stability in p-th moment of mild solutions for fractional stochastic evolution equations in Hilbert spaces by using the theory of α-order fractional resolvent operator have not been considered in the literature. In order to fill this gap, in this paper, we are concerned with the existence of saturated mild solutions and global mild solutions and also the continuous dependence of mild solutions on initial values and orders as well as the asymptotical stability in p-th moment of mild solutions for the initial value problem (IVP) of fractional stochastic evolution equations of the form…”

“…In particular, fractional stochastic evolution equations have also been studied by several authors, see [43][44][45][46][47][48][49]. Chen and Li [8] investigated the existence of α-mild solutions for a class of fractional stochastic integro-differential evolution equations with nonlocal initial conditions in a real separable Hilbert space by using Schauder fixed point theorem and approximating techniques.…”

Existence of a mild solution for an impulsive nonlocal non-autonomous neutral functional differential equation

“…In [8], author has shown the controllability of a system of impulsive semilinear non-autonomous differential equations via Rothe's type fixed-point theorem. For more details and study on such differential equation, we refer to the monographs [9,10] and papers [11][12][13][14][15][16][17][18][19][20] and reference cited therein.…”

“…By utilizing approximation techniques and fractional operator, the existence of the mild solution for nonlocal impulsive functional integro-differential equation has been established by authors in [15]. In [16], authors have considered an impulsive stochastic functional integro-differential inclusions with nonlocal conditions in a Hilbert space and provided existence results for mild solution by using approximation technique and BohnenblustKarlins fixed point theorem. In [17], authors have concerned with the existence of α-mild solutions for a fractional stochastic integro-differential equations with nonlocal initial conditions in a real separable Hilbert space by using an approximation technique.…”

“…In [17], authors have concerned with the existence of α-mild solutions for a fractional stochastic integro-differential equations with nonlocal initial conditions in a real separable Hilbert space by using an approximation technique. For more details, we refer to papers [11,[14][15][16][17][18][19][20]24,26,28] and references given therein.…”