About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 351057, 5 pages
http://dx.doi.org/10.1155/2013/351057
Research Article

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 [11 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, 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. View at Publisher · View at Google Scholar
  • 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. View at Publisher · View at Google Scholar
  • Dumitru Baleanu, H. M. Srivastava, and J. A. Tenreiro Machado, “On Local Fractional Continuous Wavelet Transform,” Abstract and Applied Analysis, 2013. View at Publisher · View at Google Scholar
  • 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. View at Publisher · View at Google Scholar
  • 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. View at Publisher · View at Google Scholar
  • 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. View at Publisher · View at Google Scholar
  • 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. 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
  • 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
  • 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. View at Publisher · View at Google Scholar