  The QCD coupling alpha_s is determined from a combined analysis of
experimental e+e- and e-p jet data confronted to theoretical predictions of the
energy evolution of the parton-to-hadron fragmentation functions (FFs) moments
--multiplicity, peak, width, skewness-- at low fractional hadron momentum z.
The impact of approximate next-to-leading order (NLO*) corrections plus
next-to-next-to-leading log (NNLL) resummations, compared to previous LO+NLL
calculations, is discussed. A global fit of the full set of existing data,
amounting to 360 FF moments at collision energies sqrt(s)~1--200 GeV, results
in alpha_s(m_Z^2)=0.1189^{+0.0025}_{-0.0014} at the Z mass.
