  The current paper presents a determination of $K^0_S$ and
$\Lambda/\bar{\Lambda}$ fragmentation functions (FFs) from QCD analysis of
single-inclusive electron-positron annihilation process (SIA). Our FFs
determinations are performed at next-to-leading order (NLO), and for the first
time, at next-to-next-to-leading order (NNLO) accuracy in perturbative Quantum
Chromodynamics (pQCD) which is designated as {\tt SAK20} FFs. Each of these FFs
is accompanied by their uncertainties which are determined using the `Hessian'
method. Considering the hadron mass corrections, we clearly investigate the
reliability of our results upon the inclusion of higher-order QCD correction.
We provide comparisons of {\tt SAK20} FFs set with the available analysis from
another group, finding in general a reasonable agreement, and also considerable
differences. In order to judge the fit quality, our theoretical predictions are
compared with the analyzed SIA datasets. {\tt SAK20} FFs at NLO and NNLO
accuracy along with their uncertainties are made available in the standard {\tt
LHAPDF} format in order to use for predictions of present and future
measurements in high-energy collisions such as LHC and RHIC.
