Hausdorff dimension

Quantum mechanics

Fixed point

Fixed-point theorem

Pure mathematics

Differential equation

Exponential stability

Applied mathematics

Hausdorff space

Hilbert space

Physics

Nonlinear system

Mathematics

Exponential function

Mathematical analysis

Semigroup

Hausdorff measure

Journal of Mathematical Analysis and Applications

In this paper, we investigate the existence and exponential stability of mild solutions for a class of impulsive neutral stochastic functional differential equations driven by fBm with noncompact semigroup in Hilbert spaces. Sufficient conditions for the existence of mild solutions are obtained using the Hausdorff measure of noncompactness and the Mönch fixed point theorem. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results.

Existence and exponential stability for impulsive neutral stochastic functional differential equations driven by fBm with noncompact semigroup via Mönch fixed point