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Article
Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives
Physics Letters A (2013)
  • Xiao-Jun Yang
  • H. M. Srivastava, H. M. Srivastava
  • J. -H. He, J. -H. He
  • D. Baleanu, D. Baleanu
Abstract

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.

Publication Date
April 8, 2013
Citation Information
X.-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.