  In this paper, we find necessary and sufficient conditions for the
boundedness of fractional maximal operator $M_{\alpha}$ on Orlicz spaces. As an
application of this results we consider the boundedness of fractional maximal
commutator $M_{b,\alpha}$ and nonlinear commutator of fractional maximal
operator $[b,M_{\alpha}]$ on Orlicz spaces, when $b$ belongs to the Lipschitz
space, by which some new characterizations of the Lipschitz spaces are given.
