  In this paper we compare the experimental HERA data with the next-to-leading
order approach (NLO) of Ref.[C.~Contreras, E.~Levin, R.~Meneses and
M.~Sanhueza,Eur. Phys. J. C 80 (2020) no.11, 1029). This approach includes the
re-summed NLO corrections to the kernel of the evolution equation, the correct
asymptotic behaviour in the NLO at $\tau = r^2 Q^2_s \,\gg\,1$; the impact
parameter dependence of the saturation scale in accord with the Froissarrt
theorem as well as the non-linear corrections. In this paper, we successfully
describe the experimental data with the quality, which is not worse, than in
the leading order fits with larger number of the phenomenological parameters.
It is demonstrated, that the data could be described, taking into account both
the diffusion on $\ln(k_T)$, which stems from perturbative QCD, and the
Gribov's diffusion in impact parameters. It is shown an ability to describe the
data at rather large values of $\alpha_S$.
