Different forms of diffusion equations on fractals proposed in the literature are reviewed and critically discussed. Variants of the known fractional diffusion equations are suggested here and worked out analytically. On the basis of these results we conclude that the quest: "what is the form of the diffusion equation on fractals," is still open, but we are possibly close to obtaining a satisfactory answer.
Roman, H. (2004). How does the diffusion equation on fractals look?. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 12(2), 149-156 [10.1142/S0218348X0400246X].
How does the diffusion equation on fractals look?
Roman H. E.
2004
Abstract
Different forms of diffusion equations on fractals proposed in the literature are reviewed and critically discussed. Variants of the known fractional diffusion equations are suggested here and worked out analytically. On the basis of these results we conclude that the quest: "what is the form of the diffusion equation on fractals," is still open, but we are possibly close to obtaining a satisfactory answer.
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