We investigate the fractional stochastic heat equation, driven by a random noise which admits a covariance measure structure with respect to the time variable and has a spatial covariance given by the Riesz kernel. This class of process includes White-colored noise, fractional colored noise and other related processes. We give a sufficient condition for the existence of the mild solution and we establish some properties of its. Then, we study the self similarity and the path regularity of this solution with respect to time variable on the particular case when the noise behaves as a fractional Brownian motion in time.

中文翻译：

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具有加性分数有色噪声的混合分数随机热方程

我们研究由随机噪声驱动的分数随机热方程，该方程允许相对于时间变量的协方差测量结构，并具有由 Riesz 核给出的空间协方差。此类过程包括白色噪声、分数有色噪声和其他相关过程。我们给出了温和溶液存在的充分条件，并建立了它的一些性质。然后，当噪声在时间上表现为分数布朗运动时，我们研究了该解相对于时间变量的自相似性和路径规律性。