Nonstandard and fractal electrodynamics in Finsler-Randers space

In this study, we have analyzed the Finsler-Randers manifolds starting from nonstandard Lagrangians formalism which is considered as an emergent phenomenon in the theory of the calculus of variations. These special forms of Lagrangians are motivating since they have explicit dependence on special function. We have proved that their associated usual geodesics on Finsler-Randers manifold are characterized by a quadratic damping and we have established its importance in classical electrodynamics. Moreover, we show that this construction can be extended for the case of fractal electrodynamics in Finsler-Randers manifolds.