2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171888We 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.14 pages, 2 tables, 10 figures. Invited talk at the 15th International Seminar on High Energy Physics "QUARKS-2008", Sergiev Posad, Russia, 23--29 May, 2008. Referrences are supplemented with HEP-Arxiv numbersHigh Energy Physics - Phenomenologytext