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.

10 pages, 3 figures

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Cited by in corpus (1)

• Dual Conformable Derivative: Definition, Simple Properties and Perspectives for Applications