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Similarity Solution for Fractional Diffusion Equation

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  • Jun-Sheng Duan
  • Ai-Ping Guo
  • Wen-Zai Yun

Abstract

Fractional diffusion equation in fractal media is an integropartial differential equation parametrized by fractal Hausdorff dimension and anomalous diffusion exponent. In this paper, the similarity solution of the fractional diffusion equation was considered. Through the invariants of the group of scaling transformations we derived the integro‐ordinary differential equation for the similarity variable. Then by virtue of Mellin transform, the probability density function p(r, t), which is just the fundamental solution of the fractional diffusion equation, was expressed in terms of Fox functions.

Suggested Citation

  • Jun-Sheng Duan & Ai-Ping Guo & Wen-Zai Yun, 2014. "Similarity Solution for Fractional Diffusion Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:548126
    DOI: 10.1155/2014/548126
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    References listed on IDEAS

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    4. Giona, Massimiliano & Eduardo Roman, H., 1992. "Fractional diffusion equation for transport phenomena in random media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 87-97.
    5. Ai-Ming Yang & Carlo Cattani & Hossein Jafari & Xiao-Jun Yang, 2013. "Analytical Solutions of the One‐Dimensional Heat Equations Arising in Fractal Transient Conduction with Local Fractional Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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