Following continuous-time random-walk dynamics, we consider particle diffusion and trapping on fractals, and study the interplay of the spatial ($\alpha$) and temporal ($\gamma$) stochastic aspects. At long times and for broad waiting-time distributions the mean squared displacement behaves as $〈r^2\mathrm{}\left(t\right)\mathrm{}〉\sim t^{\alpha \gamma }$, whereas the particle decay is algebraic, $\Phi \mathrm{}\left(t\right)\mathrm{}\sim t^{-\gamma }$.

• Received 30 April 1984

DOI:https://doi.org/10.1103/PhysRevLett.53.1301