Geometry of Curves with Fractional Derivatives in Lorentz Plane

Meltem Öğrenmiş

doi:10.53570/jnt.1087800

EN

Geometry of Curves with Fractional Derivatives in Lorentz Plane

Abstract

In this paper, the geometry of curves is discussed based on the Caputo fractional derivative in the Lorentz plane. Firstly, the tangent vector of a spacelike plane curve is defined in terms of the fractional derivative. Then, by considering a spacelike curve in the Lorentz plane, the arc length and fractional ordered frame of this curve are obtained. Later, the curvature and Frenet-Serret formulas are found for this fractional ordered frame. Finally, the relation between the fractional curvature and classical curvature of a spacelike plane curve is obtained. In the last part of the study, considering the timelike plane curve in the Lorentz plane, new results are obtained with the method in the previous section.

Keywords

Caputo fractional derivative, Tangent vectors, Frenet-Serret formulas, curvature

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Meltem Öğrenmiş ^*
0000-0002-2626-0543
Türkiye

Publication Date

March 31, 2022

Submission Date

March 14, 2022

Acceptance Date

March 28, 2022

Published in Issue

Year 2022 Number: 38

DOI

https://doi.org/10.53570/jnt.1087800

IZ

https://izlik.org/JA53MY58WT

APA

Öğrenmiş, M. (2022). Geometry of Curves with Fractional Derivatives in Lorentz Plane. Journal of New Theory, 38, 88-98. https://doi.org/10.53570/jnt.1087800

AMA

1.Öğrenmiş M. Geometry of Curves with Fractional Derivatives in Lorentz Plane. JNT. 2022;(38):88-98. doi:10.53570/jnt.1087800

Chicago

Öğrenmiş, Meltem. 2022. “Geometry of Curves With Fractional Derivatives in Lorentz Plane”. Journal of New Theory, nos. 38: 88-98. https://doi.org/10.53570/jnt.1087800.

EndNote

Öğrenmiş M (March 1, 2022) Geometry of Curves with Fractional Derivatives in Lorentz Plane. Journal of New Theory 38 88–98.

IEEE

[1]M. Öğrenmiş, “Geometry of Curves with Fractional Derivatives in Lorentz Plane”, JNT, no. 38, pp. 88–98, Mar. 2022, doi: 10.53570/jnt.1087800.

ISNAD

Öğrenmiş, Meltem. “Geometry of Curves With Fractional Derivatives in Lorentz Plane”. Journal of New Theory. 38 (March 1, 2022): 88-98. https://doi.org/10.53570/jnt.1087800.

JAMA

1.Öğrenmiş M. Geometry of Curves with Fractional Derivatives in Lorentz Plane. JNT. 2022;:88–98.

MLA

Öğrenmiş, Meltem. “Geometry of Curves With Fractional Derivatives in Lorentz Plane”. Journal of New Theory, no. 38, Mar. 2022, pp. 88-98, doi:10.53570/jnt.1087800.

Vancouver

1.Meltem Öğrenmiş. Geometry of Curves with Fractional Derivatives in Lorentz Plane. JNT. 2022 Mar. 1;(38):88-9. doi:10.53570/jnt.1087800