The primary aim of this paper is to focus on the stability analysis of an advanced neural stochastic functional differential equation with finite delay driven by a fractional Brownian motion in a Hilbert space. We examine the existence and uniqueness of mild solution of \( {\textrm{d}}\left[ {x}_{a}(s) + {\mathfrak {g}}(s, {x}_{a}(s - \omega (s)))\right] =\left[ {\mathfrak {I}}{x}_a(s) + {\mathfrak {f}}(s, {x}_a(s -\varrho (s)))\right] {\textrm{d}}s + \varsigma (s){\textrm{d}}\varpi ^{{\mathbb {H}}}(s),\) \(0\le s\le {\mathcal {T}}\), \({x}_a(s) = \zeta (s),\ -\rho \le s\le 0. \) The main goal of this paper is to investigate the Ulam–Hyers stability of the considered equation. We have also provided numerical examples to illustrate the obtained results. This article also discusses the Euler–Maruyama numerical method through two examples.

本文的主要目的是关注由希尔伯特空间中分数布朗运动驱动的具有有限延迟的高级神经随机函数微分方程的稳定性分析。我们检验\( {\textrm{d}}\left[ {x}_{a}(s) + {\mathfrak {g}}(s, {x}_{a} (s - \omega (s)))\right] =\left[ {\mathfrak {I}}{x}_a(s) + {\mathfrak {f}}(s, {x}_a(s -\ varrho (s)))\right] {\textrm{d}}s + \varsigma (s){\textrm{d}}\varpi ^{{\mathbb {H}}}(s),\) \ ( 0\le s\le {\mathcal {T}}\) , \({x}_a(s) = \zeta (s),\ -\rho \le s\le 0.\)这个的主要目标论文的目的是研究所考虑方程的 Ulam-Hyers 稳定性。我们还提供了数值示例来说明所获得的结果。本文还通过两个例子讨论了Euler-Maruyama数值方法。