Fractional approach of Maxwell equations in the curved spacetime

In this paper some basic definitions of fractional vector calculus are introduced. A fractional form of Maxwell's equations using these definitions are obtained. The first pair of Maxwell's equations are generalized. The gravity is introduced into Maxwell's equations. Some fractional covariant forms are deduced. The fractional Maxwell's field strength tensor is unchanged under a gauge transformation. Fractional continuity equation and the charge conservation are proved.