A generalization of fractional equiaffine curvatures of plane curves

Abstract

In this study, we deal with equiaffine plane curves by considering a general local fractional derivative. First, the concepts of alpha-equiaffine arc length and alpha-equiaffine curvature are introduced. In the sense of fractional calculus, equiaffine Frenet formulas and an analog of the fundamental theorem are reestablished. Finally, plane curves with constant fractional equiaffine curvature are described.