Fractional random walk lattice dynamics

We analyze time-discrete and time-continuous 'fractional' random walks on undirected regular networks with special focus on cubic periodic lattices in n = 1, 2, 3,.. dimensions. The fractional random walk dynamics is governed by a master equation involving fractional powers of Laplacian matrices ${{L}^{\frac{\alpha}{2}}}$ where $\alpha =2$ recovers the normal walk. First we demonstrate that the interval $0