The Fractal Lie Derivative: Theory and Applications
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916672480215040 |
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| author | Golmankhaneh, Alireza Khalili Hashemzadeh, Elham Cattani, Carlo O'Regan, Donal Jørgensen, Palle E. T. |
| author_facet | Golmankhaneh, Alireza Khalili Hashemzadeh, Elham Cattani, Carlo O'Regan, Donal Jørgensen, Palle E. T. |
| contents | 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 \(α\)-order differential equation are examined, followed by a discussion of the symmetries of the fractal linear \(n\)-th \(α\)-order differential equation. Additionally, the symmetries of the fractal linear first \(α\)-order differential equation are derived. Several examples are provided to illustrate and highlight the details of these concepts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01966 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Fractal Lie Derivative: Theory and Applications Golmankhaneh, Alireza Khalili Hashemzadeh, Elham Cattani, Carlo O'Regan, Donal Jørgensen, Palle E. T. General Mathematics 28A80, 35B06, 35A30 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 \(α\)-order differential equation are examined, followed by a discussion of the symmetries of the fractal linear \(n\)-th \(α\)-order differential equation. Additionally, the symmetries of the fractal linear first \(α\)-order differential equation are derived. Several examples are provided to illustrate and highlight the details of these concepts. |
| title | The Fractal Lie Derivative: Theory and Applications |
| topic | General Mathematics 28A80, 35B06, 35A30 |
| url | https://arxiv.org/abs/2504.01966 |