Fractional Cauchy problem on random snowflakes

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.