A new type electromagnetic curves in optical fiber and rotation of the polarization plane using fractional calculus

Yılmaz, Beyhan

doi:10.1016/j.ijleo.2021.168026

Cited by 21 publications

(7 citation statements)

References 22 publications

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“…Studies examining the answer to this question are still very new. For example, one of these studies examined the effect of fractional analysis on geometry [20], while another study investigated the effect of fractional analysis on electromagnetic curves in fiber optics [23]. It should be taken into account that fractional analyzes, which are claimed to offer clearer solutions numerically, can also give clearer information geometrically.…”

Section: Discussionmentioning

confidence: 99%

Special Fractional Curve Pairs with Fractional Calculus

Has

Yılmaz

2022

International Electronic Journal of Geometry

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In this study, the effect of fractional derivatives, whose application area is increasing day by day, on curve pairs is investigated. As it is known, there are not many studies on a geometric interpretation of fractional calculus. When examining the effect of fractional analysis on a curve, the Conformable fractional derivative that fits the algebraic structure of differential geometry derivative is used. This effect is examined with the help of examples consistent with the theory and visualized for different values of the Conformable fractional derivative. The difference of this study from others is the use of Conformable fractional derivatives and integrals in calculations. Fractional calculus has applications in many fields such as physics, engineering, mathematical biology, fluid mechanics,signal processing, etc. Fractional derivatives and integrals have become an extremely important and new mathematical method in solving various problems in many sciences.

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Section: Discussionmentioning

confidence: 99%

Special Fractional Curve Pairs with Fractional Calculus

Has

Yılmaz

2022

International Electronic Journal of Geometry

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“…Recently, Equations () and () have attracted the attention of a great number of scientists. So there exist many valuable papers in the literature approaching these equations in different views [24–34].…”

Section: Fermi–walker Magnetic and Electric Vector Fieldsmentioning

confidence: 99%

Fermi–Walker magnetic curves and Killing trajectories in 3D Riemannian manifolds

Demirkol

2023

Math Methods in App Sciences

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This paper deals with obtaining some new characterizations on the dynamics of the moving charged particle acting under particular forces in the three‐dimensional space. In this perspective, we have enlarged the research of magnetic curves and associated Killing magnetic fields by adding the Fermi–Walker parallelism and derivative. By doing this, we investigate the Hall–Killing–Fermi effect on the charged particle, then we define new types of Fermi–Walker magnetic curves corresponding to the Killing magnetic field. We carefully construct the Fermi–Walker character of the magnetic field to prove the parallelism of the magnetic trajectories and uniformly accelerated motion of the charged particle. It leads to defining a very special family of magnetic fields, that is, Fermi–Walker uniform magnetic fields. Moreover, we use the Killing feature of the magnetic field to show that the Frenet–Serret scalars and quasislopes of the magnetic curves must meet particular differential equations that lead to obtaining some geometric interpretations of the magnetic trajectories. Last but not the least, both of these two characters allow us to define Killing and Fermi–Walker electric vector fields influencing the motion of the charged particle experiencing the Lorentz force in the three‐dimensional setting.

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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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A new type electromagnetic curves in optical fiber and rotation of the polarization plane using fractional calculus

Cited by 21 publications

References 22 publications

Special Fractional Curve Pairs with Fractional Calculus

Special Fractional Curve Pairs with Fractional Calculus

Fermi–Walker magnetic curves and Killing trajectories in 3D Riemannian manifolds

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

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