Maxwell's equations and electromagnetic Lagrangian density in fractional form

Abstract

The fractional form of the electromagnetic Lagrangian density is presented using the Riemann-Liouville fractional derivative. Agrawal procedure is employed to obtain Maxwell's equations in fractional form. The Hamilton equations of motion resulting from the electromagnetic Lagrangian density are obtained. Conserved quantities, such as energy density, momentum, and Poynting's vector, are also derived using fractional Noether's theorem.