  It is known in scattering theory that the minimal velocity bound plays a
conclusive role in proving the asymptotic completeness of the wave operators.
In this study, we prove the minimal velocity bound and other important
estimates for the two-body Schroedinger-type operator with fractional powers.
We assume that the pairwise potential functions belong to broad classes that
include long-range decay and Coulomb-type local singularities. Our estimates
are expected to be applied to prove the asymptotic completeness for the
fractional Schroedinger-type operators in various (not only short-range but
also long-range and N-body) situations.
