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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 351057, 5 pages
Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets
1College of Mechanical Engineering, Yanshan University, Qinhuangdao 066004, China
2College of Science, Hebei United University, Tangshan 063009, China
3Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou Campus, Xuzhou, Jiangsu 221008, China
4College of Mathematics and Information Science, Qujing Normal University, Qujing, Yunnan 655011, China
Received 6 May 2013; Accepted 22 May 2013
Academic Editor: Dumitru Baleanu
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 [21 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, De-Fu Cheng, and Xiao-Jun Yang, “Approximation Solutions for Local Fractional Schrödinger Equation in the One-Dimensional Cantorian System,” Advances in Mathematical Physics, vol. 2013, pp. 1–5, 2013.
- Xiao-Jing Ma, H. M. Srivastava, Dumitru Baleanu, and Xiao-Jun Yang, “A New Neumann Series Method for Solving a Family of Local Fractional Fredholm and Volterra Integral Equations,” Mathematical Problems in Engineering, vol. 2013, pp. 1–6, 2013.
- Dumitru Baleanu, H. M. Srivastava, and J. A. Tenreiro Machado, “On Local Fractional Continuous Wavelet Transform,” Abstract and Applied Analysis, 2013.
- Sheng-Ping Yan, Hossein Jafari, and Hassan Kamil Jassim, “Local Fractional Adomian Decomposition and Function Decomposition Methods for Laplace Equation within Local Fractional Operators,” Advances in Mathematical Physics, vol. 2014, pp. 1–7, 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.
- E. M. E. Zayed, and K. A. E. Alurrfi, “The ()-Expansion Method and Its Applications to Find the Exact Solutions of Nonlinear PDEs for Nanobiosciences,” Mathematical Problems in Engineering, vol. 2014, pp. 1–10, 2014.
- Dumitru Baleanu, J. A. Tenreiro Machado, Carlo Cattani, Mihaela Cristina Baleanu, and Xiao-Jun Yang, “Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators,” Abstract and Applied Analysis, vol. 2014, pp. 1–6, 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.
- 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.
- Yu-Zhu Zhang, Ai-Min Yang, and Yue Long, “Initial Boundary Value Problem For Fractal Heat Equation In The Semi-Infinite Region By Yang-Laplace Transform,” Thermal Science, vol. 18, no. 2, pp. 677–681, 2014.
- E.M.E. Zayed, and K.A.E. Alurrfi, “A new Jacobi elliptic function expansion method for solving a nonlinear PDE describing the nonlinear low-pass electrical lines,” Chaos, Solitons & Fractals, vol. 78, pp. 148–155, 2015.
- M E Zayed Elsayed, and A E Alurrfi Khaled, “The generalized projective Riccati equations method and its applications for solving two nonlinear PDEs describing microtubules,” International Journal of Physical Sciences, vol. 10, no. 13, pp. 391–402, 2015.
- Guo-Cheng Wu, Dumitru Baleanu, Sheng-Da Zeng, and Wei-Hua Luo, “Mittag-Leffler Function for Discrete Fractional Modelling,” Journal of King Saud University - Science, 2015.
- Zheng-Biao Li, and Wei-Hong Zhu, “Fractional series expansion method for fractional differential equations,” International Journal Of Numerical Methods For Heat & Fluid Flow, vol. 25, no. 7, pp. 1525–1530, 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.
- Syed Tauseef Mohyud-Din, Naveed Ahmed, Asif Waheed, Muhammad Ali Akbar, and Umar Khan, “Solutions Of Fractional Diffusion Equations By Variation Of Parameters Method,” Thermal Science, vol. 19, pp. S69–S75, 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, Canan Ünlü, Seithuti Philemon Moshokoa, and Chaudry Masood Khalique, “Local Fractional Laplace Variational Iteration Method for Solving Diffusion and Wave Equations on Cantor Sets within Local Fractional Operators,” Mathematical Problems in Engineering, vol. 2015, pp. 1–9, 2015.
- Xiao-Jun Yang, Dumitru Baleanu, Mihailo P. Lazarevic, and Milan S. Cajic, “Fractal Boundary Value Problems For Integral And Differential Equations With Local Fractional Operators,” Thermal Science, vol. 19, no. 3, pp. 959–966, 2015.