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In this short note we prove that if $u$ solves $(\partial_t - \Delta)^s u =Vu$ in $\mathbb R^n_x \times \mathbb R_t$, and vanishes to infinite order at apoint $(x_0, t_0)$, then $u \equiv 0$ in $\mathbb R^n_x \times \mathbb R_t$.This sharpens (and completes) our earlier result that proves $u(\cdot, t)\equiv 0$ for $t \leq t_0$ if it vanishes to infinite order at $(x_0, t_0)$.

On the forward in time propagation of zeros in fractional heat type problems