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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 754248, 5 pages
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 [22 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.
- 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.
- Rabha W. Ibrahim, and Hamid A. Jalab, “Existence of Entropy Solutions for Nonsymmetric Fractional Systems,” Entropy, vol. 16, no. 9, pp. 4911–4922, 2014.
- Rabha W. Ibrahim, and Jay M. Jahangiri, “Existence and uniqueness of an attractive nonlinear diffusion system,” Applied Mathematics and Computation, 2014.
- Yu Zhang, Dumitru Baleanu, and Xiaojun Yang, “On a Local Fractional Wave Equation under Fixed Entropy Arising in Fractal Hydrodynamics,” Entropy, vol. 16, no. 12, pp. 6254–6262, 2014.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Xiao-Jun Yang, Dumitru Baleanu, and H.M. Srivastava, “Local fractional similarity solution for the diffusion equation defined on Cantor sets,” Applied Mathematics Letters, 2015.
- Zhi Zhang, Wei Wei, and JinRong Wang, “Generalization of Hermite-Hadamard Inequalities Involving Hadamard Fractional Integrals,” Filomat, vol. 29, no. 7, pp. 1515–1524, 2015.
- Sheng-Ping Yan, “Local Fractional Laplace Series Expansion Method For Diffusion Equation Arising In Fractal Heat Transfer,” Thermal Science, vol. 19, pp. S131–S135, 2015.
- Ai-Min Yang, Jie Li, Yu-Zhu Zhang, and Wei-Xing Liu, “A New Coupling Schedule For Series Expansion Method And Sumudu Transform With An Applications To Diffusion Equation In Fractal Heat Transfer,” Thermal Science, vol. 19, pp. S145–S149, 2015.
- Xiao-Jun Yang, Dumitru Baleanu, and Mihaela-Cristina Baleanu, “Observing Diffusion Problems Defined On Cantor Sets In Different Co-Ordinate Systems,” Thermal Science, vol. 19, pp. S151–S156, 2015.
- Xu Cheng, and Xiao-Xun Ma, “THE DIFFUSION MODEL OF FRACTAL HEAT AND MASS TRANSFER IN FLUIDIZED BED A Local Fractional Arbitrary Euler-Lagrange Formula,” Thermal Science, vol. 19, pp. S109–S115, 2015.
- Zhi-Ping Fan, Hassan Kamil Jassim, Ravinder Krishna Raina, and Xiao-Jun Yang, “Adomian Decomposition Method For Three-Dimensional Diffusion Model In Fractal Heat Transfer Involving Local Fractional Derivatives,” Thermal Science, vol. 19, pp. S137–S141, 2015.
- Ai-Min Yang, Yu-Zhu Zhang, and Jie Li, “Laplace Variational Iteration Method For The Two-Dimensional Diffusion Equation In Homogeneous Materials,” Thermal Science, vol. 19, pp. S163–S168, 2015.
- Shu Xu, Xiang Ling, Yang Zhao, and Hassan Kamil Jassim, “A Novel Schedule For Solving The Two-Dimensional Diffusion Problem In Fractal Heat Transfer,” Thermal Science, vol. 19, pp. S99–S103, 2015.
- Hassan Kamil Jassim, “The Approximate Solutions of Three-Dimensional Diffusion and Wave Equations within Local Fractional Derivative Operator,” Abstract and Applied Analysis, vol. 2016, pp. 1–5, 2016.