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Cantor-type cylindrical-coordinate method for differential equations with local fractional derivatives
Authors:Xiao-Jun Yang  H.M. Srivastava  Ji-Huan He  Dumitru Baleanu
Affiliation:1. Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou, Jiangsu, 221008, People?s Republic of China;2. Institute of Applied Mathematics, Qujing Normal University, Qujing 655011, People?s Republic of China;3. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada;4. National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, 199 Ren-ai Road, Suzhou 215123, People?s Republic of China;5. Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, Ankara, 06530, Turkey;6. Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, 21589, Saudi Arabia;7. Institute of Space Sciences, Magurele-Bucharest, Romania
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.
Keywords:Heat-conduction equation  Damped wave equation  Local fractional derivatives  Cantor set
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