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We give a short introduction to the Analytic Perturbation Theory (APT) inQCD, discuss its problems and how they can be resolved in Fractional APT(FAPT), and give a brief report about taking into account heavy-quarkthresholds in FAPT. Then we describe the resummation approach in the one-loopAPT and FAPT, which produces finite answers in both Euclidean and Minkowskiregions, provided the generating function P(t) of perturbative coefficients d_nis known. We consider its applications in estimations of the width of Higgsboson decay H^0\to b\bar{b} and of the Adler function D(Q^2) and the ratio R(s)in the N_f=4 region. In order to provide numerical answers we suggest verysimple factorially growing models for perturbative coefficients d_n. We seethat for the case of Higgs boson decay an accuracy of the order of 1% isreached at N^3LO approximation, when term d_3{\mathcal A}_3 is taken intoaccount. In the case of Adler function D(Q^2) we have an accuracy of the orderof 0.1% already at N^2LO (i. e., with taking into account d_2{\mathcal A}_2term). The main conclusion is: In order to achieve an accuracy of the order of1%, we do not need to calculate more than four loops and d_4 coefficients areneeded only to estimate corresponding generating functions P(t).

Resummation approach in Fractional APT: How many loops do we need to calculate?