Exponential decay for fractional Schr\"odinger parabolic problems

We discuss exponential decay in $L^p(R^N)$, $1\leq p \leq \infty$, of solutions of a fractional Schr\"odinger parabolic equation with a locally uniformly integrable potential. The exponential type of the semigroup of solutions is considered and its dependence in $1\leq p \leq \infty$ is addressed. We characterise a large class of potentials for which solutions decay exponentially.