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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.

Citations to this Article [10 citations]

The following is the list of published articles that have cited the current article.

  • Ai-Min Yang, Zeng-Shun Chen, H. M. Srivastava, and Xiao-Jun Yang, “Application of the Local Fractional Series Expansion Method and the Variational Iteration Method to the Helmholtz Equation Involving Local Fractional Derivative Operators,” Abstract and Applied Analysis, vol. 2013, pp. 1–6, 2013. View at Publisher · View at Google Scholar
  • Yang Zhao, Dumitru Baleanu, Carlo Cattani, De-Fu Cheng, and Xiao-Jun Yang, “Maxwell’s Equations on Cantor Sets: A Local Fractional Approach,” Advances in High Energy Physics, vol. 2013, pp. 1–6, 2013. View at Publisher · View at Google Scholar
  • Rabha W. Ibrahim, and Jay M. Jahangiri, “Existence and uniqueness of an attractive nonlinear diffusion system,” Applied Mathematics and Computation, 2014. View at Publisher · View at Google Scholar
  • Shun-Qin Wang, Yong-Ju Yang, and Hassan Kamil Jassim, “Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014. View at Publisher · View at Google Scholar
  • Xiao-Jun Yang, Jordan Hristov, H. M. Srivastava, and Bashir Ahmad, “Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg-de Vries Equation,” Abstract and Applied Analysis, vol. 2014, pp. 1–10, 2014. View at Publisher · View at Google Scholar
  • Long-Fei Wang, Xiao-Jun Yang, Dumitru Baleanu, Carlo Cattani, and Yang Zhao, “Fractal Dynamical Model of Vehicular Traffic Flow within the Local Fractional Conservation Laws,” Abstract and Applied Analysis, vol. 2014, pp. 1–5, 2014. View at Publisher · View at Google Scholar
  • Yong-Ju Yang, and Liu-Qing Hua, “Variational Iteration Transform Method for Fractional Differential Equations with Local Fractional Derivative,” Abstract and Applied Analysis, vol. 2014, pp. 1–9, 2014. View at Publisher · View at Google Scholar
  • Wei Wei, H. M. Srivastava, Yunyi Zhang, Lei Wang, Peiyi Shen, and Jing Zhang, “A Local Fractional Integral Inequality on Fractal Space Analogous to Anderson’s Inequality,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014. View at Publisher · View at Google Scholar
  • Guang-Sheng Chen, H. M. Srivastava, Pin Wang, and Wei Wei, “Some Further Generalizations of Hölder's Inequality and Related Results on Fractal Space,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014. View at Publisher · View at Google Scholar
  • Xian-Jin Wang, Yang Zhao, Carlo Cattani, and Xiao-Jun Yang, “Local Fractional Variational Iteration Method for Inhomogeneous Helmholtz Equation within Local Fractional Derivative Operator,” Mathematical Problems in Engineering, vol. 2014, pp. 1–7, 2014. View at Publisher · View at Google Scholar