# Structural scale $q-$derivative and the LLG-Equation in a scenario with fractionality

## TL;DR

This paper introduces a deformed version of the Landau-Lifshitz-Gilbert equation using structural derivatives to incorporate long-range interactions and fractional effects, resulting in natural damping phenomena without explicit damping terms.

## Contribution

It develops a novel deformed LLG equation employing scale q-derivative and Mittag-Leffler functions, capturing fractional and long-range effects in magnetic dynamics.

## Key findings

- Damping appears naturally without explicit Gilbert damping.
- The deformed equation accounts for long-range forces and fractional space effects.
- The approach generalizes classical LLG to fractional and non-local interactions.

## 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.