Title: Structural scale $q-$derivative and the LLG-Equation in a scenario with fractionality,
Abstract: In the present contribution, we study the Landau-Lifshitz-Gilbert equation
with two versions of structural derivatives recently proposed: the scale
$q-$derivative in the non-extensive statistical mechanics and the axiomatic
metric derivative, which presents Mittag-Leffler functions as eigenfunctions.
The use of structural derivatives aims to take into account long-range forces,
possible non-manifest or hidden interactions and the dimensionality of space.
Having this purpose in mind, we build up an evolution operator and a deformed
version of the LLG equation. Damping in the oscillations naturally show up
without an explicit Gilbert damping term.