Using the leading-twist approximation of the Wilson operator product expansion with ``frozen{''} and analytic versions of the strong-coupling constant, we show that the Bessel-inspired behavior of the structure function F-2 and its slope partial derivative In F-2/partial derivative In(1/x) at small values of x, obtained for a flat initial condition in the DGLAP evolution equations, leads to good agreement with experimental data of deepinelastic scattering at DESY HERA. (C) 2009 Elsevier B.V. All rights reserved.