Conformable Differential Geometry of Some Special Curves in the Equi-Affine Space

Anıl Altınkaya

doi:10.53570/jnt.1774470

Conformable Differential Geometry of Some Special Curves in the Equi-Affine Space

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.

Keywords

References

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Details

Primary Language

English

Subjects

Algebraic and Differential Geometry

Journal Section

Research Article

Authors

Anıl Altınkaya ^*
0000-0003-2382-6596
Türkiye

Early Pub Date

September 30, 2025

Publication Date

September 30, 2025

Submission Date

August 30, 2025

Acceptance Date

September 30, 2025

Published in Issue

Year 2025 Number: 52

DOI

https://doi.org/10.53570/jnt.1774470

IZ

https://izlik.org/JA78AP47YK

Cite

RIS / Bibtex

APA

Altınkaya, A. (2025). Conformable Differential Geometry of Some Special Curves in the Equi-Affine Space. Journal of New Theory, 52, 83-91. https://doi.org/10.53570/jnt.1774470

AMA

1.Altınkaya A. Conformable Differential Geometry of Some Special Curves in the Equi-Affine Space. JNT. 2025;(52):83-91. doi:10.53570/jnt.1774470

Chicago

Altınkaya, Anıl. 2025. “Conformable Differential Geometry of Some Special Curves in the Equi-Affine Space”. Journal of New Theory, nos. 52: 83-91. https://doi.org/10.53570/jnt.1774470.

EndNote

Altınkaya A (September 1, 2025) Conformable Differential Geometry of Some Special Curves in the Equi-Affine Space. Journal of New Theory 52 83–91.

IEEE

[1]A. Altınkaya, “Conformable Differential Geometry of Some Special Curves in the Equi-Affine Space”, JNT, no. 52, pp. 83–91, Sept. 2025, doi: 10.53570/jnt.1774470.

ISNAD

Altınkaya, Anıl. “Conformable Differential Geometry of Some Special Curves in the Equi-Affine Space”. Journal of New Theory. 52 (September 1, 2025): 83-91. https://doi.org/10.53570/jnt.1774470.

JAMA

1.Altınkaya A. Conformable Differential Geometry of Some Special Curves in the Equi-Affine Space. JNT. 2025;:83–91.

MLA

Altınkaya, Anıl. “Conformable Differential Geometry of Some Special Curves in the Equi-Affine Space”. Journal of New Theory, no. 52, Sept. 2025, pp. 83-91, doi:10.53570/jnt.1774470.

Vancouver

1.Anıl Altınkaya. Conformable Differential Geometry of Some Special Curves in the Equi-Affine Space. JNT. 2025 Sep. 1;(52):83-91. doi:10.53570/jnt.1774470