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Full-Text Articles in Physics

Maxwell’S Equations On Cantor Sets: A Local Fractional Approach, Yang Xiaojun Nov 2013

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.


Helmholtz And Diffusion Equations Associated With Local Fractional Derivative Operators Involving The Cantorian And Cantor-Type Cylindrical Coordinates, Yang Xiaojun Jul 2013

Helmholtz And Diffusion Equations Associated With Local Fractional Derivative Operators Involving The Cantorian And Cantor-Type Cylindrical Coordinates, Yang Xiaojun

Xiao-Jun Yang

The main object of this paper is to investigate the Helmholtz and diffusion equations on the Cantor sets involving local fractional derivative operators. The Cantor-type cylindrical-coordinate method is applied to handle the corresponding local fractional differential equations. Two illustrative examples for the Helmholtz and diffusion equations on the Cantor sets are shown by making use of the Cantorian and Cantor-type cylindrical coordinates.


Fractal Heat Conduction Problem Solved By Local Fractional Variation Iteration Method, Yang Xiaojun Mar 2013

Fractal Heat Conduction Problem Solved By Local Fractional Variation Iteration Method, Yang Xiaojun

Xiao-Jun Yang

This paper points out a novel local fractional variational iteration method for processing the local fractional heat conduction equation arising in fractal heat transfer.