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We review the main results on the generalization of the DGLAP evolutionequations within the cut Mellin moments (CMM) approach, which allows one toovercome the problem of kinematic constraints in Bjorken $x$. CMM obtained bymultiple integrations as well as multiple differentiations of the originalparton distribution also satisfy the DGLAP equations with the simplytransformed evolution kernel. The CMM approach provides novel tools to testQCD; here we present one of them. Using appropriate classes of CMM, weconstruct the generalized Bjorken sum rule that allows us to determine theBjorken sum rule value from the experimental data in a restricted kinematicrange of $x$. We apply our analysis to COMPASS data on the spin structurefunction $g_1$.

Cut Moments approach in the analysis of DIS data