  This talk describes the resummation approach in (Fractional) Analytic
Perturbation Theory (FAPT) in QCD. First, we make a short historical review of
the (F)APT approach and then shortly describe the global scheme of FAPT which
allows one to take into account heavy-quark thresholds. After that we show how
it is possible to resum a non-power series in (F)APT both in the one- and
two-loop approximations. As an application we suggest our analysis of the Higgs
boson decay ${H^0\to b\bar{b}}$, important for the LHC program, and of the
vector-current Adler function.
