  For $s \in [1/2, 1)$, let $u$ solve $(\partial_t - \Delta)^s u = Vu$ in
$\mathbb R^{n} \times [-T, 0]$ for some $T>0$ where $||V||_{ C^2(\mathbb R^n
\times [-T, 0])} < \infty$. We show that if for some $0< c< T$ and $\epsilon>0$
$$\frac{1}{c} \int_{[-c,0]} u^2(x, t) dt \leq Ce^{-|x|^{2+\epsilon}}\ \forall x
\in \mathbb R^n,$$ then $u \equiv 0$ in $\mathbb R^{n} \times [-T, 0]$.
