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.
Cantor-type cylindrical-coordinate method for differential equations with local fractional derivativesPhysics Letters A (2013)
Publication DateApril 8, 2013
Citation InformationX.-J. Yang, H. M. Srivastava, J. -H. He, D. Baleanu, Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives, Physics Letters A, vol. 377, no.28–30, pp. 1696–1700, 2013.