A note on fractional electrodynamics

We investigate the time evolution of the fractional electromagnetic waves by using the time fractional Maxwell’s equations. We show that electromagnetic plane wave has amplitude which exhibits an algebraic decay, at asymptotically large times.

► Fractional Lorentz force (Eq. (17)).
► Algebraic decay of electromagnetic wave’s amplitude for alpha = 1/4 (Eqs. (37)).
► Algebraic decay of electromagnetic wave’s amplitude, at asymptotically large times (Eqs. (43)).
► Fractional dynamics of charged particles (Eqs. (44), (45), (46), (47) and (48)).