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- W4302027354 abstract "Abstract Electromagnetic wave equation and the coupled Maxwell's equations are studied and solved in a fractional space-time of dimensions D , 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, ∇ 2 Ψ ( r , t ) − 1/c 2 ∂ 2 /∂t 2 Ψ ( 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 ) = − µ0 J ( 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 ." @default.
- W4302027354 created "2022-10-06" @default.
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- W4302027354 date "2022-10-05" @default.
- W4302027354 modified "2023-10-18" @default.
- W4302027354 title "Propagation of electromagnetic waves in fractional space time" @default.
- W4302027354 doi "https://doi.org/10.21203/rs.3.rs-2117906/v1" @default.
- W4302027354 hasPublicationYear "2022" @default.
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