Abstract
This study investigates the conformable differential geometry of some special curves defined in the equi-affine space. The conformable derivative, a generalization of fractional calculus, is a flexible operator controlled by a parameter $\alpha$ that enables the modeling of nonlocal behavior in functions. This paper aims to offer a new perspective by combining the modern concept of derivative with equi-affine differential geometry. First, this paper introduces the conformable equi-affine arc length parameter and the corresponding conformable Frenet frame in the equi-affine space. The main focus is on characterizing special classes of curves, such as helices, slant helices, and rectifying curves, within the conformable equi-affine frame. These results expand the geometric applications of conformable calculus and provide a broader theoretical framework for curve analysis in equi-affine geometry. Finally, the accuracy of the results is observed with an example, and the curvatures are plotted as a function of $\alpha$ with MATLAB R2022b.
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Details
| Primary Language | English |
|---|---|
| Subjects | Algebraic and Differential Geometry |
| Journal Section | Research Article |
| Authors | |
| Submission Date | August 30, 2025 |
| Acceptance Date | September 30, 2025 |
| Early Pub Date | September 30, 2025 |
| Publication Date | September 30, 2025 |
| Published in Issue | Year 2025 Issue: 52 |