  A local time decay estimate of fractional Schr\"odinger operators with slowly
decaying positive potentials are studied. It is shown that its resolvent is
smooth near zero and the time propagator has fast local time decay which is
very different from very short-range cases. The key element of the proof is to
establish a weaker Agmon estimate for a classically forbidden region using
exotic symbol calculus. As a byproduct, we prove that the Riesz operator is a
pseudodifferential operator with an exotic symbol.
