On Quaternionic Bertrand Curves in Euclidean $3$-Space

Has, Aykut; Yılmaz, Beyhan

doi:10.47000/tjmcs.1021801

Cited by 5 publications

(8 citation statements)

References 4 publications

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“…The conformable coefficients of the conformable second fundamental form defined on the conformable M surface have changed with the effect of conformable fractional analysis as seen in Eqs. ( 13), ( 14) and (15). As is known, the second fundamental form is used to describe the nonintrinsic invariants of the surface.…”

Section: Discussionmentioning

confidence: 99%

“…Especially recently, the focus has been on whether any geometric approximation can be made for fractional derivatives with Differential Geometry and Vector Analysis [12,19,32]. In addition, some special curves and characterizations of curve pairs are also investigated with fractional analysis [14,15]. Moreover, the effect of fractional analysis on magnetic curves, which is an important application area in physics, is investigated [16,33].…”

Section: Introductionmentioning

confidence: 99%

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Measurement and Calculation on Conformable Surfaces

Has,

Yılmaz

2023

Mediterr. J. Math.

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In this study, some basic concepts related to the surface are examined with the help of conformable fractional analysis. As known, the best thing that makes fractional analysis popular is that it gives numerically more approximate results compared to classical analysis. For this reason, the concepts that enable us to make calculations based on measurement on the surface have been redefined to give more numerical results with conformable fractional analysis. In addition, with the help of fractional analysis, it is explained which concepts is changed or not. Finally, an example is given to better understand the obtained results and its graph is drawn with the help of Mathematica. The reason for using conformable fractional analysis in this study is that it is more suitable for the algebraic structure of differential geometry.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Measurement and Calculation on Conformable Surfaces

Has,

Yılmaz

2023

Mediterr. J. Math.

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“…Let x = x(s) be a regular unit speed conformable curve in the Euclidean 3− space where s measures its arc length. The following relation exists between the curvature and torsion of the curve x and the conformable curvature and torsion [17]…”

Section: Preliminariesmentioning

confidence: 99%

“…For instance, Gozutok U. et al are reconstructed the Frenet frame, which is the most commonly used structure in characterizing curves, using the conformable derivative [15]. Furthermore, Has A. and Yilmaz B. are conducted in-depth studies on curves and surfaces [16][17][18][19]31]. These research works demonstrate that fractional calculus provides a different perspective in the field of geometry and that the conformable derivative is a more effective tool for understanding and characterizing the geometrical structures in fractional analyses.…”

Section: Introductionmentioning

confidence: 98%

Characterizations of Tzitzeica Curves Using Conformable Frenet Frame

Has,

Yılmaz,

Ayvacı

2023

Preprint

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Tzitzeica curve is a mathematical curve that has been used to describe the behavior of certain physical phenomena. It was first discovered by Romanian mathematician Gheorghe Tzitzeica and has since been used to model many phenomena, including the motion of a pendulum, the oscillations of a vibrating string, and the flow of electricity through a circuit. The curve is an example of what is known as an elliptic curve and can be used to analyze complex systems. Its properties make it useful in many applications, such as cryptography and data compression. In the light of this information, the aim of this study, the conditions for a conformable curve and its spherical indicator curves to be a Tzitzeica curve will be examined. Thus, by understanding the behavior of the Tzitzeica curve, researchers can gain insight into complex systems and make more accurate predictions about their behavior. MSC Classification: 26A33 , 53A04 , 53A55

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“…Gozutok U. et al are analyzed the basic concepts of curves and Frenet frame in fractional order with the help of conformable local fractional derivative [8]. On the other hand Has A. and Yılmaz B. are investigated some special curves and curve pairs in fractional order with the help of conformable Frenet frame [11,12]. In addition, electromagnetic fields and magnetic curves are investigated under fractional derivative by Has A. and Yılmaz B.…”

Section: Introductionmentioning

confidence: 99%

C α −ruled surfaces respect to direction curve in fractional differential geometry

Has

Yılmaz

Ayvacı

2023

Preprint

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Conformable fractional calculus is a relatively new branch of mathematics that seeks to extend traditional calculus to include non-integer order derivatives and integrals. This new form of calculus allows for a more precise description of physical phenomena, such as those related to fractal geometry and chaos theory. It also offers new tools for solving problems in physics, engineering, finance, and other areas. By using conformable fractional calculus, researchers can gain insight into the behavior of systems that would otherwise be difficult or impossible to analyze. In this article, we will discuss the fundamentals of conformable fractional calculus and its applications in various fields. For this purpose ruled surfaces are studied with conformable fractional calculus. The ruled surface is rearranged concerning the conformable surface definition and geometric properties are investigated. MSC Classification: 53A04 , 53A05 , 26A33

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On Quaternionic Bertrand Curves in Euclidean $3$-Space

Cited by 5 publications

References 4 publications

Measurement and Calculation on Conformable Surfaces

Measurement and Calculation on Conformable Surfaces

Characterizations of Tzitzeica Curves Using Conformable Frenet Frame

C α −ruled surfaces respect to direction curve in fractional differential geometry

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