Abstract

HAS, Aykut  and  YILMAZ, Beyhan. Effect of fractional analysis on magnetic curves. Rev. mex. fis. [online]. 2022, vol.68, n.4, 041401.  Epub May 19, 2023. ISSN 0035-001X.  https://doi.org/10.31349/revmexfis.68.041401.

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 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.

Keywords : Magnetic curve; vector fields; fractional derivative; conformable fractional derivative.