Let us deal with the positive solutions of
\begin{equation*}
\frac{\partial u(t)}{\partial t}=k(t)\Delta _{\alpha }u(t)+h(t)u^{1+\beta
}(t),\text{ \ }u(0,x)=\varphi (x)\geq 0,\text{ }x\in \mathbb{R}^{d},
\end{equation*}
where $\Delta _{\alpha }$ is the fractional Laplacian, $0<\alpha \leq 2$,
and $\beta >0$ is a constant. We prove that under certain regularity
condition on $\varphi $, $h$ and $k$ any non-trivial positive solution blows
up in finite time. In this way we answer, in particular, the question raised
in [4] for the critical case.