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Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators

Author

Listed:
  • Dumitru Baleanu
  • J. A. Tenreiro Machado
  • Carlo Cattani
  • Mihaela Cristina Baleanu
  • Xiao-Jun Yang

Abstract

We perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

Suggested Citation

  • Dumitru Baleanu & J. A. Tenreiro Machado & Carlo Cattani & Mihaela Cristina Baleanu & Xiao-Jun Yang, 2014. "Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:535048
    DOI: 10.1155/2014/535048
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    References listed on IDEAS

    as
    1. Ai-Min Yang & Xiao-Jun Yang & Zheng-Biao Li, 2013. "Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-5, June.
    2. Ai-Min Yang & Xiao-Jun Yang & Zheng-Biao Li, 2013. "Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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    Cited by:

    1. Hassan Kamil Jassim, 2016. "The Approximate Solutions of Three‐Dimensional Diffusion and Wave Equations within Local Fractional Derivative Operator," Abstract and Applied Analysis, John Wiley & Sons, vol. 2016(1).
    2. Mohammed Al-Refai & Mohamed Ali Hajji & Muhammad I. Syam, 2014. "An Efficient Series Solution for Fractional Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Xiao-Feng Niu & Cai-Li Zhang & Zheng-Biao Li & Yang Zhao, 2014. "Local Fractional Derivative Boundary Value Problems for Tricomi Equation Arising in Fractal Transonic Flow," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    4. Ai-Min Yang & Yu-Zhu Zhang & Xiao-Long Zhang, 2014. "The Nondifferentiable Solution for Local Fractional Tricomi Equation Arising in Fractal Transonic Flow by Local Fractional Variational Iteration Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    5. Li Chen & Yang Zhao & Hossein Jafari & J. A. Tenreiro Machado & Xiao-Jun Yang, 2014. "Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    6. Guang-Sheng Chen & H. M. Srivastava & Pin Wang & Wei Wei, 2014. "Some Further Generalizations of Hölder′s Inequality and Related Results on Fractal Space," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    7. Shao-Hong Yan & Xiao-Hong Chen & Gong-Nan Xie & Carlo Cattani & Xiao-Jun Yang, 2014. "Solving Fokker‐Planck Equations on Cantor Sets Using Local Fractional Decomposition Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    8. Wei Wei & H. M. Srivastava & Yunyi Zhang & Lei Wang & Peiyi Shen & Jing Zhang, 2014. "A Local Fractional Integral Inequality on Fractal Space Analogous to Anderson’s Inequality," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    9. X. Y. Li & B. Y. Wu & R. T. Wang, 2014. "Reproducing Kernel Method for Fractional Riccati Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    10. H. M. Srivastava & Alireza Khalili Golmankhaneh & Dumitru Baleanu & Xiao-Jun Yang, 2014. "Local Fractional Sumudu Transform with Application to IVPs on Cantor Sets," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    11. Meng Li & Xiao-Feng Hui & Carlo Cattani & Xiao-Jun Yang & Yang Zhao, 2014. "Approximate Solutions for Local Fractional Linear Transport Equations Arising in Fractal Porous Media," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).

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