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

作者:Zhao, Yang; Baleanu, Dumitru; Cattani, Carlo; Cheng, De-Fu*; Yang, Xiao-Jun
来源:Advances in High Energy Physics, 2013, 2013: 686371.
DOI:10.1155/2013/686371

摘要

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.