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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 754248, 5 pages
http://dx.doi.org/10.1155/2013/754248
Research Article

Helmholtz and Diffusion Equations Associated with Local Fractional Derivative Operators Involving the Cantorian and Cantor-Type Cylindrical Coordinates

1College of Science, Yanshan University, Qinhuangdao 066004, China
2Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada V8W 3R4
3Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar 47415-416, Iran
4Department of Mathematics and Mechanics, China University of Mining and Technology, Jiangsu, Xuzhou 221008, China

Received 9 June 2013; Accepted 7 July 2013

Academic Editor: J. A. Tenreiro Machado

Copyright © 2013 Ya-Juan Hao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The main object of this paper is to investigate the Helmholtz and diffusion equations on the Cantor sets involving local fractional derivative operators. The Cantor-type cylindrical-coordinate method is applied to handle the corresponding local fractional differential equations. Two illustrative examples for the Helmholtz and diffusion equations on the Cantor sets are shown by making use of the Cantorian and Cantor-type cylindrical coordinates.