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Maxwell’S Equations On Cantor Sets: A Local Fractional Approach, Yang Xiaojun
Maxwell’S Equations On Cantor Sets: A Local Fractional Approach, Yang Xiaojun
Xiao-Jun Yang
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.