This paper aims to investigate the controllability for impulsive neutral stochastic delay partial differential equations (PDEs) driven by fractional Brownian motion (fBm) with Hurst index [Formula: see text] and Lévy noise in Hilbert spaces. By using a fixed point approach without imposing a severe compactness condition on the semigroup, a new set of sufficient conditions is derived. The results in this paper are generalization and continuation of the recent results on this issue. At the end, an application to the stochastic nonlinear heat equation with delays driven by a fBm and Lévy noise is given.

中文翻译：

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由 fBm 和 Lévy 噪声驱动的脉冲中性随机延迟偏微分方程的可控性

本文旨在研究由分数布朗运动 (fBm) 驱动的脉冲中性随机延迟偏微分方程 (PDE) 的可控性，其中赫斯特指数 [公式：见正文] 和希尔伯特空间中的 Lévy 噪声。通过使用不动点方法而不对半群施加严格的紧致性条件，导出了一组新的充分条件。本文的结果是对该问题最近结果的概括和延续。最后，给出了由 fBm 和 Lévy 噪声驱动的随机非线性热方程的应用。