Maxwell’s Equations on Cantor Sets : A Local Fractional Approach

Abstract EN

Maxwell’s equations on Cantor sets are derived from the local fractional vector calculus.

It is shown that Maxwell’s equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields.

Local fractional differential forms of Maxwell’s equations on Cantor sets in the Cantorian and Cantor-type cylindrical coordinates are obtained.

Maxwell's equations on Cantor set with local fractional operators are the first step towards a unified theory of Maxwell’s equations for the dynamics of cold dark matter.