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Cantor-Type Cylindrical-Coordinate Method For Differential Equations With Local Fractional Derivatives, Xiao-Jun Yang
Cantor-Type Cylindrical-Coordinate Method For Differential Equations With Local Fractional Derivatives, Xiao-Jun Yang
Xiao-Jun Yang
In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.