  In this contribution, we build up an axiomatic local metric derivative that
exhibits the Mittag-Leffler as an eigenfunction and is valid for low-level
fractionality, whenever the order parameter is close to $1$. This version of
deformed or metric derivative may be a possible alternative to the versions by
Jumarie and the inappropriately so-called local fractional derivative also
based on the Jumarie's approach. With rules similar to the classical ones, but
with a solid axiomatic basis in the limit pointed out here, we present our
results and some comments on the limits of validity for the controversial
formalism found in the literature of the area.
