Effect of fractional analysis on magnetic curves

Abstract

In this present paper, the effect of fractional analysis on magnetic curves is researched. A magnetic field is defined by the property that its divergence is zero in a three dimensional Riemannian manifold. We investigate the trajectories of the magnetic fields called as t-magnetic, n-magnetic and b-magnetic curves according to fractional derivative and integral. 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 magnetic curve, the conformable fractional derivative that best 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.

Characterizations of Tzitzeica Curves Using Conformable Frenet Frame

“…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.…”

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

“…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].…”

A non-Newtonian magnetic curves in multiplicative Riemann manifolds

“…Bozkurt Z. et al conducted an investigation into N-magnetic curves and B-magnetic curves in 3D Riemann manifolds [29][30][31]. Magnetic curves have been a subject of study by researchers across various disciplines and within diverse spatial contexts [32][33][34][35][36][37].…”