A determination of the longitudinal structure function $F_{L}$ from the parametrization of $F_{2}$ based on the Laplace transformation

I calculate the longitudinal structure function, using Laplace transform techniques, from the parametrization of the structure function $F_{2}(x,Q^{2})$ and its derivative at low values of the Bjorken variable $x$. I consider the effect of the charm quark mass to the longitudinal structure function, which leads to rescaling variable for $n_{f}=4$. The results are compared with the H1 collaboration data and the CTEQ-Jefferson Lab (CJ) collaboration [Phys.Rev.D {\bf93}, 114017 (2016)] parametrization model. The obtained results with the Bjorken variable of $x$ are found to be comparable with the results L.P.Kaptari et al. [Phys.Rev.D {\bf99}, 096019 (2019)] which is based on the Mellin transform techniques.

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