Journal
PHYSICS LETTERS A
Volume 377, Issue 28-30, Pages 1696-1700Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physleta.2013.04.012
Keywords
Heat-conduction equation; Damped wave equation; Local fractional derivatives; Cantor set
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Funding
- PAPD (Priority Academic Program Development of Jiangsu Higher Education Institutions)
- Project for Six Kinds of Top Talents in Jiangsu Province, China [ZBZZ-035]
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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. (c) 2013 Published by Elsevier B.V.
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