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.