Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives

• A novel Cantor-type cylindrical-coordinate method is first proposed.
• Differential equations are converted to Cantor-type cylindrical-coordinate systems.
• Heat-conduction and damped wave equations are analyzed.

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.