Global attractiveness and exponential stability for impulsive fractional neutral stochastic evolution equations driven by fBm

Jiankang Liu,Wei Xu,Qin Guo

doi:10.1186/s13662-020-2520-7

Abstract

This paper is concerned with a class of fractional neutral stochastic integro-differential equations with impulses driven by fractional Brownian motion (fBm). First, by means of the resolvent operator technique and contraction mapping principle, we can directly show the existence and uniqueness result of mild solution for the aforementioned system. Then we develop a new impulsive-integral inequality to obtain the global attracting set and pth moment exponential stability for this type of equation. Worthy of note is that this powerful inequality after little modification is applicable to the case with delayed impulses. Moreover, sufficient conditions which guarantee the pth moment exponential stability for some pertinent systems are stated without proof. In the end, an example is worked out to illustrate the theoretical results.

Highlights

In recent two decades, fractional stochastic evolution equations have grabbed the attention of many researchers, owing to their applications in various fields, such as physics, chemistry, viscoelasticity, heat conduction, aerodynamics, electrodynamics of complex medium, electricity mechanics, and so forth
It is worth noting that Deng and Shu [20] established an impulsive-integral inequality to obtain the exponential stability of mild solution to impulsive neutral stochastic functional differential equations driven by fractional Brownian motion (fBm) with noncompact semigroup
6 Conclusion In this paper, by establishing a new impulsive-integral inequality, we obtain the global attracting sets and some sufficient conditions which guarantee the pth moment exponential stability of mild solutions for impulsive fractional neutral stochastic integro-differential equations driven by fBm and standard Bm

Summary

Introduction

Fractional stochastic evolution equations have grabbed the attention of many researchers, owing to their applications in various fields, such as physics, chemistry, viscoelasticity, heat conduction, aerodynamics, electrodynamics of complex medium, electricity mechanics, and so forth (see, e.g., [1,2,3,4] and the references therein). [13], Long et al [14] examined the global attractiveness and exponential stability of impulsive stochastic neutral evolution equations driven by Q-Wiener process.

Results

Conclusion