  We study analytically, in one dimension, the survival probability $P_{s}(t)$
up to time $t$ of an immobile target surrounded by mutually noninteracting
traps each performing a continuous-time random walk (CTRW) in continuous space.
We consider a general CTRW with symmetric and continuous (but otherwise
arbitrary) jump length distribution $f(\eta)$ and arbitrary waiting time
distribution $\psi(\tau)$. The traps are initially distributed uniformly in
space with density $\rho$. We prove an exact relation, valid for all time $t$,
between $P_s(t)$ and the expected maximum $E[M(t)]$ of the trap process up to
time $t$, for rather general stochastic motion $x_{\rm trap}(t)$ of each trap.
When $x_{\rm trap}(t)$ represents a general CTRW with arbitrary $f(\eta)$ and
$\psi(\tau)$, we are able to compute exactly the first two leading terms in the
asymptotic behavior of $E[M(t)]$ for large $t$. This allows us subsequently to
compute the precise asymptotic behavior, $P_s(t)\sim a\, \exp[-b\,
t^{\theta}]$, for large $t$, with exact expressions for the stretching exponent
$\theta$ and the constants $a$ and $b$ for arbitrary CTRW. By choosing
appropriate $f(\eta)$ and $\psi(\tau)$, we recover the previously known results
for diffusive and subdiffusive traps. However, our result is more general and
includes, in particular, the superdiffusive traps as well as totally anomalous
traps.
