  We show that the parabolic equation $u_t + (-\Delta)^s u = q(x)
|u|^{\alpha-1} u$ posed in a time-space cylinder $(0,T) \times \mathbb{R}^N$
and coupled with zero initial condition and zero nonlocal Dirichlet condition
in $(0,T) \times (\mathbb{R}^N \setminus \Omega)$, where $\Omega$ is a bounded
domain, has at least one nontrivial nonnegative finite energy solution provided
$\alpha \in (0,1)$ and the nonnegative bounded weight function $q$ is separated
from zero on an open subset of $\Omega$. This fact contrasts with the
(super)linear case $\alpha \geq 1$ in which the only bounded finite energy
solution is identically zero.
