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Dergiler / 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
Sayfa
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Yayın Tarihi
2021-04-15
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Several examples are also given by figures.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri: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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Sonuç & Katkı:Several examples are also given by figures.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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