In this paper, we investigate stochastic evolution equations with unbounded delay in fractional power spaces perturbed by a tempered fractional Brownian motion \(B_Q^{\sigma ,\lambda }(t)\) with \(-1/2<\sigma <0\) and \(\lambda >0\). We first introduce a technical lemma which is crucial in our stability analysis. Then, we prove the existence and uniqueness of mild solutions by using semigroup methods. The upper nonlinear noise excitation index of the energy solutions at any finite time t is also obtained. Finally, we consider the exponential asymptotic behavior of mild solutions in mean square.

中文翻译：

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具有无穷时滞和回火分数布朗运动的发展方程解的指数行为和上噪声激励指数。

在本文中，我们研究了分数幂空间中无穷时滞的随机演化方程，该分数幂空间受到回火分数布朗运动\（B_Q ^ {\ sigma，\ lambda}（t）\）的\（-1/2 <\ sigma < 0 \）和\（\ lambda> 0 \）。我们首先介绍一个技术引理，这对我们的稳定性分析至关重要。然后，我们使用半群方法证明了温和溶液的存在性和唯一性。还获得了在任何有限时间t处能量解的较高的非线性噪声激励指数。最后，我们考虑了均方中温和解的指数渐近行为。