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

Abstract

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.

Keywords

• Global attracting set
• Exponential stability
• Fractional neutral stochastic integro-differential equations
• Caputo fractional derivative
• Delayed impulses