  Through data analysis, we present new sets of nonperturbative fragmentation
functions (FFs) for $\Lambda_c^+$ baryon both at leading and next-to-leading
order (NLO) and, for the first time, at next-to-next-to-leading order (NNLO) in
the minimal subtraction factorization scheme with five massless quarks. The FFs
are determined by fitting all available data of inclusive single $\Lambda_c^+$
baryon production in $e^+e^-$ annihilation taken by the OPAL Collaboration at
CERN LEP1 and Belle Collaboration at KEKB. We also estimate the uncertainties
in the $\Lambda_c^+$ FFs as well as in the corresponding observables. In a
completely different approach based on the Suzuki model, we will theoretically
calculate the $\Lambda_c^+$ FF from charm quark and present our result at
leading order perturbative QCD framework. A comparison confirms a good
consistency between both approaches. We will also apply the $\Lambda_c^+$ FFs
to make theoretical predictions for the energy distribution of $\Lambda_c^+$
produced through the top quark decay, to be measured at the CERN LHC.
