  We give a short introduction to the Analytic Perturbation Theory (APT) in
QCD, describe its problems and suggest as a tool for their resolution the
Fractional APT (FAPT). We also describe shortly how to treat heavy-quark
thresholds in FAPT. As an applications of this technique we discuss (i) the
pion form factor calculation in the Euclidean FAPT and (ii) the Higgs boson
decay $H^0\to b\bar{b}$ in Minkowskian FAPT. We conclude with comparison of
both approaches, Euclidean and Minkowskian FAPT.
