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.
Maxwell’s Equations on Cantor Sets: A Local Fractional ApproachAdvances in High Energy Physics (2013)
Publication DateNovember 7, 2013
Citation Information Y. Zhao, D. Baleanu, C. Cattani, D. F. Cheng, X. -J Yang, Maxwell’s Equations on Cantor Sets: A Local Fractional Approach, Advances in High Energy Physics, 2013 Article ID 686371, 6 pages, 2013.