Analysis of DIS structure functions of the nucleon within truncated Mellin moments approach

We present generalized evolution equations and factorization in terms of the truncated Mellin moments (TMM) of the parton distributions and structure functions. We illustrate the $x$ and $Q^2$ dependence of TMM in the polarized case. Using the TMM approach we compare the integrals of $g_1$ with HERMES and COMPASS data from the limited $x$-ranges.