Conformable special curves in Euclidean 3-space

Has, Aykut; Yılmaz, Beyhan; Akkurt, Abdullah; Yıldırım, Hüseyin

doi:10.2298/fil2214687h

Cited by 8 publications

(3 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

See 1 more Smart Citation

Characterizations of Tzitzeica Curves Using Conformable Frenet Frame

Has,

Yılmaz,

Ayvacı

2023

Preprint

View full text Add to dashboard Cite

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

show abstract

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Characterizations of Tzitzeica Curves Using Conformable Frenet Frame

Has,

Yılmaz,

Ayvacı

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…This approach is given by milici and Machado, [34]. 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.

View full text Add to dashboard Cite

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.

show abstract

Utilizing the Caputo fractional derivative for the flux tube close to the neutral points

Durmaz,

Ceyhan,

Özdemir

et al. 2024

Math Methods in App Sciences

View full text Add to dashboard Cite

This study examines how fractional derivatives affect the theory of curves and related surfaces, an application area that is expanding daily. There has been limited research on the geometric interpretation of fractional calculus. The present study applied the Caputo fractional calculation method, which has the most suitable structure for geometric computations, to examine the effect of fractional calculus on differential geometry. The Caputo fractional derivative of a constant is zero, enabling the geometric solution and understanding of many fractional physical problems. We examined flux tubes, which are magnetic surfaces that incorporate these lines of magnetic fields as parameter curves. Examples are visualized using mathematical programs for various values of Caputo fractional analysis, employing theory‐related examples. Fractional derivatives and integrals are widely utilized in various disciplines, including mathematics, physics, engineering, biology, and fluid dynamics, as they yield more numerical results than classical solutions. Also, many problems outside the scope of classical analysis methods can be solved using the Caputo fractional calculation approach. In this context, applying the Caputo fractional analytic calculation method in differential geometry yields physically and mathematically relevant findings, particularly in the theory of curves and surfaces.

show abstract

Conformable special curves in Euclidean 3-space

Cited by 8 publications

References 15 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

Utilizing the Caputo fractional derivative for the flux tube close to the neutral points

Contact Info

Product

Resources

About