  We show that if $u$ solves the fractional parabolic equation $(\partial_t -
\Delta )^s u = Vu$ in $B_5 \times (-25, 0]$ ($0<s<1$) such that $u(\cdot, 0)
\not\equiv 0$, then the maximal vanishing order of $u$ in space-time at $(0,0)$
is upper bounded by $C\left(1+\|V\|_{C^{1}_{(x,t)}}^{1/2s}\right)$. As $s \to
1$, it converges to the sharp maximal order of vanishing due to
Donnelly-Fefferman and Bakri. This quantifies a space like strong unique
continuation result recently proved in [3]. The proof is achieved by means of a
new quantitative Carleman estimate that we derive for the corresponding
extension problem combined with a quantitative monotonicity in time result and
a compactness argument.
