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

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International Electronic Journal of Geometry
Volume:14 Issue:1
Differential Geometry of Curves in Euclidean 3-Space with Fractional Order

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

Authors : Muhittin Evren AYDIN, Mehmet BEKTAŞ, Alper ÖĞREMİŞ, Asıf YOKUŞ

Pages : 132-144

View : 113 | Download : 6

Publication Date : 2021-04-15

Article Type : Research Paper

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.
Keywords : Fractional derivative, space curves, fundamental theorem, curvature, torsion

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