  We present NNFF1.0, a new determination of the fragmentation functions (FFs)
of charged pions, charged kaons, and protons/antiprotons from an analysis of
single-inclusive hadron production data in electron-positron annihilation. This
determination, performed at leading, next-to-leading, and
next-to-next-to-leading order in perturbative QCD, is based on the NNPDF
methodology, a fitting framework designed to provide a statistically sound
representation of FF uncertainties and to minimise any procedural bias. We
discuss novel aspects of the methodology used in this analysis, namely an
optimised parametrisation of FFs and a more efficient $\chi^2$ minimisation
strategy, and validate the FF fitting procedure by means of closure tests. We
then present the NNFF1.0 sets, and discuss their fit quality, their
perturbative convergence, and their stability upon variations of the kinematic
cuts and the fitted dataset. We find that the systematic inclusion of
higher-order QCD corrections significantly improves the description of the
data, especially in the small-$z$ region. We compare the NNFF1.0 sets to other
recent sets of FFs, finding in general a reasonable agreement, but also
important differences. Together with existing sets of unpolarised and polarised
parton distribution functions (PDFs), FFs and PDFs are now available from a
common fitting framework for the first time.
