Abstract
In this paper, by employing the fractional power of operators, semigroup theory, and fixed point strategy we obtain some new criteria ensuring the existence and exponential stability of a class of impulsive neutral stochastic integrodifferential equations driven by a fractional Brownian motion. We establish some new sufficient conditions that ensure the exponential stability of mild solution in the mean square moment by utilizing an impulsive integral inequality. Also, we provide an example to show the efficiency of the obtained theoretical result.
Highlights
The theory and applications of impulsive differential equations have undergone a rapid development in recent years
It is important and necessary to consider both time delays and impulsive effects when investigating the stability of the dynamical systems, since impulsive perturbations can affect the dynamical behavior of the system [3]
Boufoussi and Hajji [23] established the existence, uniqueness, and exponential decay to zero in mean square moment for the mild solutions to neutral stochastic differential equations driven by a fractional Brownian motion
Summary
The theory and applications of impulsive differential equations have undergone a rapid development in recent years. Boufoussi and Hajji [23] established the existence, uniqueness, and exponential decay to zero in mean square moment for the mild solutions to neutral stochastic differential equations driven by a fractional Brownian motion. Chen et al [36] examined the exponential stability of neutral stochastic partial functional differential equations with impulsive effects. This paper, inspired by the works mentioned, addresses the existence and stability problems for neutral stochastic integrodifferential systems driven by an fBm with delays and impulsive effects. T(t – tk)Ik x tk– + T(t – s)σ (s) dBHQ (s) P-a.s. To guarantee the existence and uniqueness of the solution, we impose some hypotheses: (H1) A is the infinitesimal generator of an analytic semigroup (T(t))t≥0 of bounded linear operators on the Hilbert space X and satisfies 0 ∈ σ (A).
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