Abstract
A generalized fractional diffusion equation (FDE) is presented, which describes the time-evolution of the spatial distribution of a particle performing continuous time random walk (CTRW) on a fractal lattice. For a case corresponding to the CTRW with waiting time distribution that behaves as <TEX>$\psi(t) \sim (t) ^{-(\alpha+1)}$</TEX>, the FDE is solved to give analytic expressions for the Green’s function and the mean squared displacement (MSD). In agreement with the previous work of Blumen et al. [Phys. Rev. Lett. 1984, 53, 1301], the time-dependence of MSD is found to be given as < <TEX>$r^2(t)$</TEX> > ~ <TEX>$t ^{2\alpha/dw}$</TEX>, where <TEX>$d_w$</TEX> is the walk dimension of the given fractal. A Monte-Carlo simulation is also performed to evaluate the range of applicability of the proposed FDE.
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