The existence, uniqueness and asymptotic stability of solutions to fractional stochastic impulsive neutral systems

Abstract

The paper presents novel results concerning mild solutions to fractional stochastic impulsive neutral systems, focusing on their existence, uniqueness, and asymptotic stability.
A general existence and uniqueness theorem of mild solutions is established by utilizing the method of Picard successive approximation.
Moreover, sufficient conditions regarding the impulse intensity and frequency is derived to achieve asymptotic stability for fractional stochastic impulsive neutral systems in mean-square, assuming a Lipschitz condition.
Ultimately, the theoretical results are confirmed through numerical examples.