  To study the heavy quark production processes, we use the transverse momentum
dependent (TMD, or unintegrated) gluon distribution function in a proton
obtained recently using the Kimber-Martin-Ryskin prescription from the
Bessel-inspired behavior of parton densities at small Bjorken $x$ values. We
obtained a good agreement of our results with the latest HERA experimental data
for reduced cross sections $\sigma^{c\overline{c}}_{\rm red}(x,Q^2)$ and
$\sigma^{b\overline{b}}_{\rm red}(x,Q^2)$, and also for deep inelastic
structure functions $F_2^c(x,Q^2)$ and $F_2^b(x,Q^2)$ in a wide range of $x$
and $Q^2$ values. Comparisons with the predictions based on the
Ciafaloni-Catani-Fiorani-Marchesini evolution equation and with the results of
conventional pQCD calculations performed at first three orders of perturbative
expansion are presented.
