  We investigate the energy losses of $b$ and $c$ quarks at hard collisions
with gluons and light quarks in quark-gluon plasma produced in central $Au +
Au$ collisions at RHIC energy($\sqrt{s_{NN}} = 200$ GeV). As the coupling
constant at hard collision in the perturbative QCD is limited by Landau pole at
momenta $Q^{2} = \Lambda^{2}$, we use the analytic models of QCD, where the
Landau pole is absent. We calculate the energy losses of $b$ and $c$ quarks in
analytic model of QCD at $Q^{2} \ge \Lambda^{2}$. At calculations we use the
effective quasiparticle model. We use at calculations of total nuclear
modification factor $R_{AA}^{b+c}$ the fragmentation of $b$ and $c$ quarks into
heavy hadrons with accounting theirs energy losses. We show that this factor
gives the considerably suppression of heavy $B$ and $D$ mesons in the region of
middle meanings of $p_{\perp}$. The experimental data \cite{2} show, that
nonphotonic electrons have the analogous suppression in the same region of
$p_{\perp}$.
