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arXiv · 2504.01966

The Fractal Lie Derivative: Theory and Applications

Alireza Khalili Golmankhaneh·Elham Hashemzadeh·Carlo Cattani·Donal O'Regan·Palle E. T. Jørgensen
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Abstract

This paper presents a new Lie theoretic approach to fractal calculus, which in turn yields such new results as a Fractal Noether's Theorem, a setting for fractal differential forms, for vector fields, and Lie derivatives, as well as k-fractal jet space, and algorithms for k-th fractal prolongation. The symmetries of the fractal nonlinear \(n\)-th \(\alpha\)-order differential equation are examined, followed by a discussion of the symmetries of the fractal linear \(n\)-th \(\alpha\)-order differential equation. Additionally, the symmetries of the fractal linear first \(\alpha\)-order differential equation are derived. Several examples are provided to illustrate and highlight the details of these concepts.

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Alireza Khalili Golmankhaneh, Elham Hashemzadeh, Carlo Cattani, Donal O'Regan, Palle E. T. Jørgensen. 2025-03-19. The Fractal Lie Derivative: Theory and Applications. https://arxiv.org/abs/2504.01966

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