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We obtain some new characterizations of a variable version of Lipschitzspaces in terms of the boundedness of commutators of sharp maximal functions,fractional maximal functions or fractional maximal commutators in the contextof the variable Lebesgue spaces, where the symbols of the commutators belong tothe variable Lipschitz space. A useful tool is that a symbol $b$ belongs avariable Lipschitz space of pointwise type if and only if $b$ belongs to avariable Lipschitz space of integral type.

Characterization of Lipschitz Space via the Commutators of Fractional Maximal Functions on Variable Lebesgue Spaces