Fractional equiaffine curvatures of curves in 3-dimensional affine space

Abstract

In this study, we investigate the equiaffine invariants of a parameterized curve in the 3-dimensional affine space R³   by using Caputo fractional derivative operator. We introduce the so-called fractional equiaffine arclength function for a non-degenerate parametrized curve, providing the fractional equiaffine equations of Frenet type. Furthermore, we give the relations between the fractional and standard equiaffine curvatures.