- International Electronic Journal of Geometry
- Vol: 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 Öğremiş, Asıf Yokuş
Pages : 132-144
View : 8 | Download : 3
Publication Date : 2021-04-15
Article Type : Research
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