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

Abstract

In this paper, for a given curve in the Euclidean 3-space 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 R-3 and then construct the ways of determining a curve in R-2 and R-3 in terms of the new invariants. Several examples are also given by figures.