On the new conformable optical ferromagnetic and antiferromagnetic magnetically driven waves

Using fractional differential geometry, we define different types of conformable magnetic curves to discuss some geometric features of the motion of the charged particle when its geometry is induced by the conformable fractional derivative. We obtain the non-stretching motions and the inextensibility conditions of the conformable curves to focus on their evolutions. Then, as a special case, we obtain the time evolution of the Frenet–Serret vectors of the conformable curves with respect to the optical ferromagnetic and antiferromagnetic cases. Finally, we focus on the time evolution of conformable curves under the case of the optical ferromagnetic and antiferromagnetic conditions to investigate how the anholonomy density is associated with the magnetic flux flow.