scholarly journals Fractional differential forms

2001 ◽  
Vol 42 (5) ◽  
pp. 2203 ◽  
Author(s):  
Kathleen Cottrill-Shepherd ◽  
Mark Naber
Keyword(s):  
Differential Forms ◽  
Fractional Differential ◽  
Fractional Differential Forms

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

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Yang Zhao ◽  
Dumitru Baleanu ◽  
Carlo Cattani ◽  
De-Fu Cheng ◽  
Xiao-Jun Yang
Keyword(s):  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Cold Dark Matter ◽  
Differential Forms ◽  
Cantor Sets ◽  
Unified Theory ◽  
Fractional Operators ◽  
Vector Calculus ◽  
Electric And Magnetic Fields ◽  
Fractional Differential

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.

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