  We discuss inclusive production of open charm mesons in proton-proton
scattering at the BNL RHIC. The calculation is performed in the framework of
$k_t$-factorization approach which effectively includes higher-order pQCD
corrections. Different models of unintegrated gluon distributions (UGDF) from
the literature are used. We focus on UGDF models favoured by the LHC data and
on a new up-to-date parametrizations based on the HERA collider DIS
high-precision data. Results of the $k_t$-factorization approach are compared
to next-to-leading order collinear predictions. The hadronization of heavy
quarks is done by means of fragmentation function technique. The theoretical
transverse momentum distributions of charmed mesons are compared with recent
experimental data of the STAR collaboration at $\sqrt{s} = 200$ and $500$ GeV.
Theoretical uncertainties related to the choice of renormalization and
factorization scales as well as due to the quark mass are discussed. Very good
description of the measured integrated cross sections and differential
distributions is obtained for the Jung setB$0$ CCFM UGDF. Revised charm and
bottom theoretical cross sections corresponding to those measured recently by
the STAR and PHENIX collaborations for semileptonic decays of $D$ and $B$
mesons are presented. Significant improvement in theoretical description of the
non-photonic electrons measurements is clearly obtained with respect to the
previous studies within the $k_{t}$-factorization.
