  The longitudinal proton structure function, $F_L(x,Q^2)$, from the $k_t$
factorization formalism by using the unintegrated parton distribution functions
(UPDF) which are generated through the
  KMR and MRW procedures. The LO UPDF of the KMR prescription is extracted, by
taking into account the PDF of Martin et al, i.e. MSTW2008-LO and
  MRST99-NLO and next, the NLO UPDF of the MRW scheme is generated through the
set of MSTW2008-NLO PDF as the inputs. The different aspects of
  $F_L(x,Q^2)$ in the two approaches, as well as its perturbative and
non-perturbative parts are calculated. Then the comparison of $F_L(x,Q^2)$ is
made with the data given by the ZEUS and H1 collaborations. It is demonstrated
that the extracted $F_L(x,Q^2)$ based on the UPDF of two schemes, are
consistent to the experimental data, and by a good approximation, they are
independent to the input PDF. But the one developed from the KMR prescription,
have better agreement to the data with respect to that of MRW. As it has been
suggested, by lowering the factorization scale or the Bjorken variable in the
related experiments, it may be possible to analyze the present theoretical
approaches more accurately.
