In this paper, we determine the precise fragmentation functions (FFs) of charged pions ($\pi ^\pm$), charged kaons ($K^\pm$), proton/antiprotons ($p/\bar{p}$) as well as unidentified light charged hadrons ($h^\pm$). This determination is performed through a simultaneous QCD analysis of all available experimental data from single-inclusive hadron production in electron-positron annihilation (SIA) processes for $\pi^\pm, K^\pm, p/\bar{p}$ and $h^\pm$ production. Our results show that these data have significant impact on both size and uncertainties of the FFs. We apply higher-order perturbative QCD corrections up to next-to-next-to-leading order (NNLO)
and also include finite-hadron mass effects.