  The charm structure function, ($F_2^{c\overline{c}}(x, Q^2)$), is calculated
in the framework of the $k_t$-factorization formalism by using the unintegrated
parton distribution functions (UPDF), which are generated through the Kimber et
al. (KMR) and Martin et al. (MRW) procedures. The Martin group (MMHT2014)
parton distribution functions (PDF) is used as the input PDF for the
corresponding UPDF. The resulted $F_2^{c\overline{c}}(x, Q^2)$ is compared with
the predicted data and the calculations given by the ZEUS and H1
collaborations, the parton pQCD theory, i.e. the general-mass
variable-flavour-number scheme (GMVFNS), the LO collinear procedure and the
saturation model introduced by Golec-Biernat and W\"usthoff (GBW),
respectively. In general, it is shown that the calculated charm structure
functions based on the stated above two UPDF schemes are consistent with the
experimental data and other theoretical predictions. Also, a short discussion
is presented regarding the KMR and MRW UPDF behaviors.
