In this paper, the long-time behavior of the Cesaro mean of the fundamental solution for fractional Heat equation corresponding to random time changes in the Brownian motion is studied. We consider both stable subordinators leading to equations with the Caputo-Djrbashian fractional derivative and more general cases corresponding to differential-convolution operators, in particular, distributed order derivatives.

中文翻译：

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关于分数热方程

在本文中，研究了分数布朗方程的基本解的切萨罗平均值的长期行为，该分数与布朗运动中的随机时间变化相对应。我们考虑了两个稳定的从属变量，它们导致了具有Caputo-Djrbashian分数阶导数的方程，并且考虑了对应于微分卷积算符（尤其是分布阶导数）的更一般的情况。