\(\mathcal{C}_\alpha\)-Rectifying Curves in a New Conformable Differential Geometry

Authors

  • Aykut Has Department of Mathematics, Faculty of Science, Kahramanmaras Sutcu Imam University, 46100, Kahramanmaras, Turkey
  • Beyhan Yilmaz Department of Mathematics, Faculty of Science, Kahramanmaras Sutcu Imam University, 46100, Kahramanmaras, Turkey
  • Thabet Abdeljawad Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5864

Keywords:

Fractional calculus, Conformable fractional calculus, Frenet frame, Rectifying curve, Spherical curve

Abstract

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.

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Differential Geometry

License

Copyright (c) 2025 Aykut Has, Beyhan Yilmaz, Thabet Abdeljawad

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How to Cite

\(\mathcal{C}_\alpha\)-Rectifying Curves in a New Conformable Differential Geometry. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5864. https://doi.org/10.29020/nybg.ejpam.v18i2.5864