Axiomatic Local Metric Derivatives for Low-Level Fractionality with Mittag-Leffler Eigenfunctions

In this contribution, we build up an axiomatic local metric derivative that exhibits Mittag-Leffler function 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 worked out by Jumarie and the so-called local fractional derivative also based on Jumarie's approach. With rules similar to the classical ones, but with a systematic 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.