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I use a direct method to extract the longitudinal structure function in thenext-to-leading order approximation with respect to the number of active flavorfrom the parametrization of parton distributions. The contribution of charm andbottom quarks corresponding to the gluon distributions (i.e.,$G_{n_{f}=3}(x,Q^{2})$ and $G_{n_{f}=5}(x,Q^{2})$) is considered. I compare theobtained longitudinal structure function at $n_{f}=4$ with the H1 data[Eur.Phys.J.C{\bf74}, 2814(2014) and Eur.Phys.J.C{\bf71}, 1579 (2011)] and theresult L.P.Kaptari et al.[ Phys.Rev.D{\bf 99}, 096019(2019)] which is based onthe Mellin transforms. These calculations compared with the results  from CT18 [Phys.Rev.D103, 014013(2021)] parametrization model. The nonlineareffects on the gluon distribution improve the behavior of the longitudinalstructure function in comparison with the H1 data and CT18 at low values of$Q^{2}$.

Effect of the parameterization of the distribution functions on the longitudinal structure function at small $x$