Existence results for impulsive neutral stochastic functional integro-differential inclusions with infinite delays

Abstract

In this paper, we prove the existence of mild solutions for a class of impulsive neutral stochastic functional integro-differential inclusions with infinite delays in Hilbert spaces. The results are obtained by using the fixed-point theorem for multi-valued operators due to Dhage. An example is provided to illustrate the theory. MSC: 93B05; 93E03

Existence results for an impulsive fractional integro-differential equation with state-dependent delay

“…The perturbations are conducted separately and their term is insignificant in correlation with the aggregate length of time of the procedures. For additional purposes of enthusiasm on this concept and on its uses, see for example the treatise by Lakshmikantham et al [2], Stamova [3], Graef et al [4], Bainov and Covachev [5], Benchohra et al [6] and the papers [7][8][9][10][11][12][13][14][15][16], and the references cited therein.…”

Impulsive fractional stochastic differential inclusions driven by sub-Fractional Brownian motion with infinite delay and sectorial operators

“…Therefor, we must move from deterministic problems to stochastic ones. As the generalization of classic impulsive differential and partial differential inclusions, impulsive stochastic differential and partial differential inclusions have attracted the researchers great interest, and some works have done on the existence results of mild solutions for these equation (see [24] [31] and references therein). Recently, attempts were made to combine fractional derivatives and stochastic differential inclusions.…”

On solutions set of a multivalued stochastic differential equation

“…[1], [2], [13], [7], [17], [19], [21], [20], [26]. To model uncertain systems, the multivalued stochastic differential equations (abbreviation MSDEs) [3], [6], [8], [12], [22], [24], [27]- [29] are also applied and they generalize the classical (single-valued) stochastic differential equations. Here the uncertainties, which are incorporated in MSDEs, are a stochastic uncertainty coming from random noises and an uncertainty driven by multivalued mappings.…”