  We apply (Fractional) Analytic Perturbation Theory (FAPT) to the QCD analysis
of the nonsinglet nucleon structure function $F_2(x,Q^2)$ in deep inelastic
scattering up to the next leading order and compare the results with ones
obtained within the standard perturbation QCD. Based on a popular
parameterization of the corresponding parton distribution we perform the
analysis within the Jacobi Polynomial formalism and under the control of the
numerical inverse Mellin transform. To reveal the main features of the FAPT
two-loop approach, we consider a wide range of momentum transfer from high
$Q^2\sim 100 {\rm GeV}^2$ to low $Q^2\sim 0.3 {\rm GeV}^2$ where the approach
still works.
