  In contrast to the coupling parameter in the usual perturbative QCD (pQCD),
the coupling parameter in the analytic QCD models has cuts only on the negative
semiaxis of the Q^2-plane (where q^2 = -Q^2 is the momentum squared), thus
reflecting correctly the analytic structure of the spacelike observables. The
Minimal Analytic model (MA, named also APT) of Shirkov and Solovtsov removes
the nonphysical cut (at positive Q^2) of the usual pQCD coupling and keeps the
pQCD cut discontinuity of the coupling at negative Q^2 unchanged. In order to
evaluate in MA the physical QCD quantities whose perturbation expansion
involves noninteger powers of the pQCD coupling, a specific method of
construction of MA analogs of noninteger pQCD powers was developed by Bakulev,
Mikhailov and Stefanis (BMS). We present a construction, applicable now in any
analytic QCD model, of analytic analogs of noninteger pQCD powers; this method
generalizes the BMS approach obtained in the framework of MA. We need to know
only the discontinuity function of the analytic coupling (the analog of the
pQCD coupling) along its cut in order to obtain the analytic analogs of the
noninteger powers of the pQCD coupling, as well as their timelike (Minkowskian)
counterparts. As an illustration, we apply the method to the evaluation of the
width for the Higgs decay into b+(bar b) pair.
