In this paper we compare the experimental HERA data with the next-to-leading order approach (NLO) of [Eur. Phys. J. C 80, 1029 (2020)EPCFFB1434-604410.1140/epjc/s10052-020-08580-w]. This approach includes the re-summed NLO corrections to the kernel of the evolution equation, the correct asymptotic behavior in the NLO at t=r2Qs2»1; the impact parameter dependence of the saturation scale in accord with the Froissarrt theorem as well as the nonlinear 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(kT), 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 a¯S.