Abstract. The QCD coupling α 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