  The behavior of the charm and bottom structure functions
($F_{k}^{i}(x,Q^{2})$, i=c,b; k=2,L) at small-$x$ is considered with respect to
the hard-Pomeron and saturation models. Having checked that this behavior
predicate the heavy flavor reduced cross sections concerning the unshadowed and
shadowed corrections. We will show that the effective exponents for the
unshadowed and saturation corrections are independent of $x$ and $Q^{2}$, and
also the effective coefficients are dependent to $\ln{Q^{2}}$ compared to
Donnachie-Landshoff (DL) and color dipole (CD) models.
