Abstract Abad:

In this talk I shall revisit the well-known derivation of the fractional subdiffusion equation from the CTRW model with a long-tailed waiting time distribution. Taking this derivation as a starting point, we shall derive a fractional reaction-subdiffusion equation (FRSE) for the case where the diffusing walkers are subject to a stochastic first-order evanescence (death) process governed by a time-dependent rate constant. The FRSE differs significantly from its counterpart for classical diffusion, as it contains a mixed reaction-transport term. However, it can be reduced to a pure subdiffusion equation via a suitable variable transformation, much in the spirit of Danckwerts' solution of the classical diffusion equation with a linear reaction term. We shall subsequently deal with an application of possible relevance for predator-prey models and animal foraging,namely the computation of the survival probability of an immobile target immersed in a sea of evanescent, fully absorbing traps which move subdiffusively. Time permitting, I shall briefly discuss extended results corresponding to the situation where the target is also allowed to move, thereby restricting ourselves to the case of non-evanescent subdiffusive traps.