A generalization of fractional equiaffine curvatures of plane curves - Ogrenmis, Meltem (World Scientific Publ Co Pte Ltd, 2026)
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.
Keywords: Fractional derivative; equiaffine plane curves; fundamental theorem; equiaffine arc length; equiaffine curvature