Fractional Curvatures of Equiaffine Curves in Three-Dimensional Affine Space

Abstract

This paper presents a method for computing the curvatures of equiaffine curves in three-dimensional affine space by utilizing local fractional derivatives. First, the concepts of $\\alpha$-equiaffine arc length and $\\alpha$-equiaffine curvatures are introduced by considering a general local involving conformable derivative, V-derivative, etc. In fractional calculus, equiaffine Frenet formulas and curvatures are reestablished. Then, it presents the relationships between the equiaffine curvatures and $\\alpha$-equiaffine curvatures. Furthermore, graphical representations of equiaffine and $\\alpha$-equiaffine curvatures illustrate their behavior under various conditions.