We consider the motion of particles which are scattered by randomly distributed obstacles. In between scattering events the particles move uniformly. The governing master equation is obtained by mapping the problem onto a master equation which was previously devised for the description of anomalous diffusion of particles with inertia [R. Friedrich et al., Phys. Rev. Lett. 96, 230601 (2006)]. We show that for a scale-free distance distribution of scatterers a time-fractional master equation arises. The corresponding diffusion equation which exhibits a power-law diffusion coefficient is solved in $d$ dimensions via the method of subordination.

• Received 29 May 2009

DOI:https://doi.org/10.1103/PhysRevE.80.011137