  As a lot of studies have declared, the proton structure function $F_2$
explicitly satisfies a power-law mathematical formation. We describe the
behavior of proton structure function $F_2$ at small-$x$ as well as large $Q^2$
using the analytical solution of the Balitsky-Kovchegov equation. We obtain the
effective slope value $\lambda$ of the structure function with $Q^2$. Our
results come from fitting the HERA experimental data at low $Q^2$ region and we
also give the prediction for the effective slope of $F_2$ at the high $Q^2$
region.
