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Resummation in QCD Fractional Analytic Perturbation Theory

We describe the generalization of Analytic Perturbation Theory (APT) for QCD observables, initiated by Radyushkin, Krasnikov, Pivovarov, Shirkov and Solovtsov, to fractional powers of coupling -- Fractional APT (FAPT). The basic aspects of FAPT is shortly summarized. We describe how to treat heavy-quark thresholds in FAPT and then show how to resum perturbative series in both the one-loop APT and FAPT. As an application we consider FAPT description of the Higgs boson decay $H^0\to b\bar{b}$. The main conclusion is: To achieve an accuracy of the order of 1% it is enough to take into account up to the third correction.