Electromagnetic wave equation and the coupled Maxwell's equations are studied and solved in a fractional space-time of dimensionsD, 0 < D ≤ 3 and < β ≤ 1.
We use the Green's function definition and the Fourier transform method to nd the solutions of the potentials by solving a non-homogenous partial differential equation in a fractional dimensional space-time, ∇2Ψ(r,t) − 1/c2 ∂2/∂t2Ψ(r,t) = − ƒ(r,t), where ƒ(r,t) = − ρ(r,t)/∈0 for Ψ(r,t) is the scalar potential Φ(r,t) and ƒ(r,t) = − µ0J(r,t) for Ψ(r,t) is the vector potential A(r,t). In this case we can determine the electric field E and the magnetic field B from the solutions of Φ(r,t) and A(r,t), . It is shown that the time required for the wave to propagate from the source point to the observation point is t − t́ ≥ |r − ŕ|/c,|, where c is the speed of light, ŕ is the displacement vector which define the distribution of source, r is the position vector to the observation point, t́ and t are the turning on the source and the observation times respectively, if and only if −1 ≤ D/2 + β − 2 < 1/2.