  It is well-known that the dominant mechanism to produce hadronic bound states
with large transverse momentum is fragmentation. This mechanism is described by
the fragmentation functions (FFs) which are the universal and
process-independent functions. Here, we review the perturbative FFs formalism
as an appropriate tool for studying these hadronization processes and detail
the extension of this formalism at next-to-leading order (NLO). Using the
Suzuki's model, we calculate the perturbative QCD FF for a heavy quark to
fragment into a S-wave heavy meson at NLO. As an example, we study the LO and
NLO FFs for a charm quark to split into the S-wave $D$-meson and compare our
analytic results both with experimental data and well-known phenomenological
models.
