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

Year 2021, Volume: 14 Issue: 1, 132 - 144, 15.04.2021

Muhittin Evren Aydın , Mehmet Bektaş , Alper Öğremiş , Asıf Yokuş

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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