Analysis of fractional magnetized force field flow in a unit sphere via Fermi-Walker fractional derivative

This study explores the differential geometry of a charged particle’s motion on a unit sphere S 2 within specific force fields, incorporating fractional calculus. It formulates the fractional derivative for spherical vector fields, characterizes magnetic flows via Lorentz fractional forces, and obtains the parallel transport law and constant-velocity motion equations for spherical fractional curves through fractional differentiation.