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Helmholtz and Diffusion Equations Associated with Local Fractional Derivative Operators Involving the Cantorian and Cantor‐Type Cylindrical Coordinates

Author

Listed:
  • Ya-Juan Hao
  • H. M. Srivastava
  • Hossein Jafari
  • Xiao-Jun Yang

Abstract

The main object of this paper is to investigate the Helmholtz and diffusion equations on the Cantor sets involving local fractional derivative operators. The Cantor‐type cylindrical‐coordinate method is applied to handle the corresponding local fractional differential equations. Two illustrative examples for the Helmholtz and diffusion equations on the Cantor sets are shown by making use of the Cantorian and Cantor‐type cylindrical coordinates.

Suggested Citation

  • Ya-Juan Hao & H. M. Srivastava & Hossein Jafari & Xiao-Jun Yang, 2013. "Helmholtz and Diffusion Equations Associated with Local Fractional Derivative Operators Involving the Cantorian and Cantor‐Type Cylindrical Coordinates," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlamp:v:2013:y:2013:i:1:n:754248
    DOI: 10.1155/2013/754248
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    References listed on IDEAS

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    5. Ming-Sheng Hu & Ravi P. Agarwal & Xiao-Jun Yang, 2012. "Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, December.
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