We consider time-changed Brownian motions on random Koch (pre-fractal and fractal) domains where the time change is given by the inverse to a subordinator. In particular, we study the fractional Cauchy problem with Robin condition on the pre-fractal boundary obtaining asymptotic results for the corresponding fractional diffusions with Robin, Neumann and Dirichlet boundary conditions on the fractal domain.

中文翻译：

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随机雪花上的分数柯西问题

我们考虑随机Koch（预分形和分形）域上的时变布朗运动，其中时间变化是由下级的反函数给出的。特别地，我们研究了分形前边界上具有Robin条件的分数柯西问题，并获得了分形域上Robin，Neumann和Dirichlet边界条件下相应分数阶扩散的渐近结果。