  In this work, we study the constraining power of future lepton colliders on
fragmentation functions (FFs) to light charged hadrons from quarks and gluon in
the framework of QCD collinear factorization. We perform analyses of FFs by
including a wide range of pseudo--data from future lepton colliders, such as
measurements on hadron multiplicities in the inclusive production of two jets
and $W$ boson pairs, at various center of mass energies, and from hadronic
decays of the Higgs boson, including both to heavy quarks and to gluons. The
high luminosity and high energies of future lepton colliders allow for quark
flavor separations and ensure a precise determination of FFs based solely on
data from electron-positron collisions. We find that either CEPC, FCC-$ee$ or
ILC can significantly reduce the uncertainties of FFs in a wide kinematic
range, compared to the NPC23 set obtained with a global analyses to current
world data. We also discuss the impact of higher-order QCD corrections, and the
potential constraints from measurements of three-jet production. Furthermore,
we describe an update of the FMNLO program allowing for calculating hadron
production cross sections at next-to-next-to-leading order in QCD, which is
used in this study.
