Decay at infinity for solutions to some fractional parabolic equations

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