Some properties of a fractal-time continuous-time random walk in the presence of traps

The CTRW has often been applied to problems related to transport in a statistically homogeneous disordered medium, which means that there are no traps or reflecting boundaries to be found in the medium. Two physical applications, one to the migration of photons in a turbid medium and the second to the theory of diffusion-controlled reactions in a random medium, suggest that it might be useful to study properties of the CTRW, particularly as they refer to survival probability in the presence of a trap or a trapping surface. We calculate a number of these properties when the pausing-time density is asymptotically proportional to a stable law, i.e., ψ(t)∼T^α+1 as (t/T)→∞, where 0<α<1. A forthcoming paper will establish the correspondence between properties of the CTRW and proprties of random walkers on a fractal with trapping boundaries.