\(\mathcal{C}_α\)-Rectifying Curves in a New Conformable Differential Geometry (European Journal of Pure and Applied Mathematics, 2025)
In this study we reintroduce  the theory of curves by incorporating local fractional calculus. We elucidate the condition for a naturally parametrized curve to be conformable, we define the orthonormal conformable frame of such a curve at any given point. Then we provide a comprehensive explanation of how these newly derived conformable geometric concepts are related to their classical counterparts. Furthermore, we introduce the concept of a conformable rectifying curve and provide its characterizations in terms of this differentiation with respect to arbitrary order. Some illustrative graphs are provided.
Keywords: Fractional calculus, Conformable fractional calculus, Frenet frame, Rectifying curve, Spherical curve