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Journals / International Electronic Journal of Geometry / 2026 / Volume: 14 Issue: 1

Differential Geometry of Curves in Euclidean 3-Space with Fractional Order

Muhittin Evren Aydın(FIRAT ÜNİVERSİTESİ)0000-0001-9337-8165
Mehmet Bektaş(FIRAT UNIVERSITY)0000-0002-5797-4944
Alper Öğremiş(FIRAT UNIVERSITY)0000-0001-5008-2655
Asıf Yokuş(FIRAT UNIVERSITY)0000-0001-7568-2251
Pages
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Publication Date
2021-04-15
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Several examples are also given by figures.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, for a given curve in the Euclidean 3-space $\mathbb{R}^{3}$ we introduce new invariants such as arc-length, curvature and torsion with fractional-order and provide certain relations between these and the standart invariants.
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Key Findings & Data:We obtain the Frenet-Serret formulas in $\mathbb{R}^{3}$ and then construct the ways of determining a curve in $\mathbb{R}^{2}$ and $% \mathbb{R}^{3}$ in terms of the new invariants.
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Conclusion & Impact:Several examples are also given by figures.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fractional derivative · space curves · fundamental theorem

Abstract

In this paper, for a given curve in the Euclidean 3-space $\mathbb{R}^{3}$ we introduce new invariants such as arc-length, curvature and torsion with fractional-order and provide certain relations between these and the standart invariants. We obtain the Frenet-Serret formulas in $\mathbb{R}^{3}$ and then construct the ways of determining a curve in $\mathbb{R}^{2}$ and $% \mathbb{R}^{3}$ in terms of the new invariants. Several examples are also given by figures.

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Cite This Article

Aydın, M. E., Bektaş, M., Öğremiş, A., Yokuş, A. (2021). Differential Geometry of Curves in Euclidean 3-Space with Fractional Order. International Electronic Journal of Geometry, Volume: 14 Issue: 1. https://ajindex.com/articles/1411111

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