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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 259125, 6 pages
Application of the Local Fractional Series Expansion Method and the Variational Iteration Method to the Helmholtz Equation Involving Local Fractional Derivative Operators
1College of Science, Hebei United University, Tangshan 063009, China
2College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China
3School of Civil Engineering and Architecture, Chongqing Jiaotong University, Chongqing 400074, China
4Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3R4
5Department of Mathematics and Mechanics, China University of Mining and Technology, Jiangsu, Xuzhou 221008, China
Received 31 July 2013; Accepted 17 October 2013
Academic Editor: Bashir Ahmad
Copyright © 2013 Ai-Min Yang 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 [13 citations]
The following is the list of published articles that have cited the current article.
- M. De la Sen, “On Nonnegative Solutions of Fractional -Linear Time-Varying Dynamic Systems with Delayed Dynamics,” Abstract and Applied Analysis, vol. 2014, pp. 1–19, 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.
- Ai-Min Yang, Jie Li, H. M. Srivastava, Gong-Nan Xie, and Xiao-Jun Yang, “Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative,” Discrete Dynamics in Nature and Society, vol. 2014, pp. 1–8, 2014.
- Ai-Min Yang, Yu-Zhu Zhang, Carlo Cattani, Gong-Nan Xie, Mohammad Mehdi Rashidi, Yi-Jun Zhou, and Xiao-Jun Yang, “Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets,” Abstract and Applied Analysis, vol. 2014, pp. 1–6, 2014.
- Li Chen, Yang Zhao, Hossein Jafari, J. A. Tenreiro Machado, and Xiao-Jun Yang, “Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables,” Abstract and Applied Analysis, vol. 2014, pp. 1–7, 2014.
- Meng Li, Xiao-Feng Hui, Carlo Cattani, Xiao-Jun Yang, and Yang Zhao, “Approximate Solutions for Local Fractional Linear Transport Equations Arising in Fractal Porous Media,” Advances in Mathematical Physics, vol. 2014, pp. 1–8, 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.
- 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.
- Ai-Min Yang, Yu-Zhu Zhang, and Xiao-Long Zhang, “The Nondifferentiable Solution for Local Fractional Tricomi Equation Arising in Fractal Transonic Flow by Local Fractional Variational Iteration Method,” Advances in Mathematical Physics, vol. 2014, pp. 1–6, 2014.
- Adem Kılıçman, and Wedad Saleh, “Some generalized Hermite-Hadamard type integral inequalities for generalized s-convex functions on fractal sets,” Advances in Difference Equations, vol. 2015, no. 1, 2015.
- 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.
- Adem Kılıçman, and Wedad Saleh, “Notions of generalized s-convex functions on fractal sets,” Journal of Inequalities and Applications, vol. 2015, no. 1, 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.