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Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg‐de Vries Equation

Author

Listed:
  • Xiao-Jun Yang
  • Jordan Hristov
  • H. M. Srivastava
  • Bashir Ahmad

Abstract

A mathematical model of fractal waves on shallow water surfaces is developed by using the concepts of local fractional calculus. The derivations of linear and nonlinear local fractional versions of the Korteweg‐de Vries equation describing fractal waves on shallow water surfaces are obtained.

Suggested Citation

  • Xiao-Jun Yang & Jordan Hristov & H. M. Srivastava & Bashir Ahmad, 2014. "Modelling Fractal Waves on Shallow Water Surfaces via Local Fractional Korteweg‐de Vries Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:278672
    DOI: 10.1155/2014/278672
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    References listed on IDEAS

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    1. Chun-Ying Long & Yang Zhao & Hossein Jafari, 2014. "Mathematical Models Arising in the Fractal Forest Gap via Local Fractional Calculus," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. 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).
    3. Ai-Min Yang & Zeng-Shun Chen & H. M. Srivastava & Xiao-Jun Yang, 2013. "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, Hindawi, vol. 2013, pages 1-6, November.
    4. 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, Hindawi, vol. 2014, pages 1-7, June.
    5. Ai-Min Yang & Zeng-Shun Chen & H. M. Srivastava & Xiao-Jun Yang, 2013. "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, John Wiley & Sons, vol. 2013(1).
    6. Shun-Qin Wang & Yong-Ju Yang & Hassan Kamil Jassim, 2014. "Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, January.
    7. Chun-Ying Long & Yang Zhao & Hossein Jafari, 2014. "Mathematical Models Arising in the Fractal Forest Gap via Local Fractional Calculus," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, March.
    8. Shun-Qin Wang & Yong-Ju Yang & Hassan Kamil Jassim, 2014. "Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
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    Cited by:

    1. Yuan Cao & Wei-Gang Ma & Lian-Chuan Ma, 2014. "Local Fractional Functional Method for Solving Diffusion Equations on Cantor Sets," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Nabard Habibi & Zohre Nouri, 2020. "Application of Local Fractional Homotopy Perturbation Method in Physical Problems," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).

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