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

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 withfractional-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 alsogiven 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 withfractional-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 alsogiven by figures.

Keywords

Fractional derivative space curves fundamental theorem curvature torsion

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Cite This Article

YOKUŞ, A., AYDIN, M. E., BEKTAŞ, M., ÖĞRENMİŞ, A. O. (2022). Differential Geometry of Curves in Euclidean 3-Space with Fractional Order. International Electronic Journal of Geometry, Cilt: 14 - Sayı: 1, 132–144. https://ajindex.com/articles/539592

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