Non-singlet Q²-evolution by inverse Mellin transform in the analytic perturbation theory

We discuss the application of the analytic approach called the fractional Analytic Perturbation Theory (APT) to the QCD analysis of the non-singlet structure function xF₃(x,Q²). The inverse Mellin transform method applyed for the fit of experimental data and for estimation of the Jacobi polynomial method accuracy in extraction of values of the scale parameter Λ_QCD and the form of the xF₃ structure function. Our estimates give the accuracy of the Jacobi polynomials method for the x-shape of the structure function about 10%, and accuracy for the scale parameter Λ_QCD 4%. (paper)