Obtaining fractional electromagnetic curves in optical fiber using fractional alternative moving frame

Yılmaz, Beyhan; Has, Aykut

doi:10.1016/j.ijleo.2022.169067

Cited by 14 publications

(8 citation statements)

References 22 publications

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“…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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Section: Introductionmentioning

confidence: 98%

Characterizations of Tzitzeica Curves Using Conformable Frenet Frame

Has,

Yılmaz,

Ayvacı

2023

Preprint

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“…In [35,36], Has et al investigated the many special curves by using conformable fractional derivatives. Electromagnetic curves and some special magnetic curves with the help of fractional derivatives, [37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Fractional approach to evolution of the magnetic field lines near the magnetic null points

Durmaz,

Özdemir,

Sekerci

2024

Phys. Scr.

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In this work, the magnetic reconnection model near null points in 3D space will be investigated using fractional calculations in the 3D magnetohydrodynamic framework. For the initial magnetic configuration (without external currents), we reformulated the numerically solved boundary initial value problem using fractional calculations. We studied the 3D Magnetic reconnection states and the behavior of the magnetic field around the null point and the null line. We also analyzed the fractional significance of charged particle motions in Killing magnetic fields. Moreover, the obtained results were visualized, and a comparison was made between the results obtained from integer and fractional calculations.

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“…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]. Although there are many types of fractional derivatives, the geometry of curves and surfaces can be explained more clearly thanks to differentiation rules such as the product rule and quotient rule in conformable fractional derivatives.…”

Section: Introductionmentioning

confidence: 99%

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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Obtaining fractional electromagnetic curves in optical fiber using fractional alternative moving frame

Cited by 14 publications

References 22 publications

Characterizations of Tzitzeica Curves Using Conformable Frenet Frame

Characterizations of Tzitzeica Curves Using Conformable Frenet Frame

Fractional approach to evolution of the magnetic field lines near the magnetic null points

Measurement and Calculation on Conformable Surfaces

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