In this work we present a generalized multi-index derivative, which contains as particular cases, with an index, several local derivatives known from the literature (both conformable and non-conformable). Obviously this new development contains many of the desirable properties of integer derivatives. It is worth noting that the multi-index differential operator departs from the classic single-order local derivatives, as in the case of the particular cases presented, which leads to an adequate and useful mathematical tool to generalize widely accepted results, with applications potentials to Physics, fundamental within mathematical simulation.
