  We consider the survival probability $f(t)$ of a random walk with a constant
hopping rate $w$ on a host lattice of fractal dimension $d$ and spectral
dimension $d_s\le 2$, with spatially correlated traps. The traps form a
sublattice with fractal dimension $d_a<d$ and are characterized by the
absorption rate $w_a$ which may be finite (imperfect traps) or infinite
(perfect traps). Initial coordinates are chosen randomly at or within a fixed
distance of a trap. For weakly absorbing traps ($w_a\ll w$), we find that
$f(t)$ can be closely approximated by a stretched exponential function over the
initial stage of relaxation, with stretching exponent $\alpha=1-(d-d_a)/d_w$,
where $d_w$ is the random walk dimension of the host lattice. At the end of
this initial stage there occurs a crossover to power law kinetics $f(t)\sim
t^{-\alpha}$ with the same exponent $\alpha$ as for the stretched exponential
regime. For strong absorption $w_a>w$, including the limit of perfect traps
$w_a\to \infty$, the stretched exponential regime is absent and the decay of
$f(t)$ follows, after a short transient, the aforementioned power law for all
times.
