A fractionally magnetized flow of force fields and Fermi-Walker conformable derivative on the unit sphere

Abstract

In this study, we aim to investigate the differential geometric aspect of the motion of the charged particle, when it is exposed to particular force fields on the unit sphere S-2, by considering the effect of the fractional calculus. We describe the conformable fractional derivative formula of the spherical vector fields moving along with the charged particle along with its trajectory. Moreover, we characterize the magnetic flows of the charged particle associated with the dynamical spherical conformable curve by defining Lorentz conformable force on the unit sphere S-2. Finally, we obtain the parallel transportation rule and uniformness of the motion occurring along with the spherical conformable curve in view of fractional derivatives.