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摘要: 根据连续性方程，可以得到分形上的标准扩散方程。然而这个标准扩散方程并不能真正描述分形介质中的反常扩散，其根源在于分形介质中的扩散具有记忆效应，为了得到更普遍的扩散方程，通过讨论早期提出的扩散方程的缺陷，可以得到分数阶扩散方程，并且更具有普遍性。Abstract: We derive the standard diffusion equation from the continuity equation and by discussing the defectiveness of earlier proposed equations. We get the generalized fractional diffusion equation for anomalous transport.
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Key words:
- fractal lattice /
- probability density /
- fractal anomalous transport
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Roman H E, Giona M. J Phys A, 1992, 25: 2107. Havlin S, Ben-Avraham D. Advances in Physics, 1987, 36: 695. O'Shaughnessy B, Procaccia I. Phys Rev Lett, 1985 54: 455. Giona M, Roman H E. Physica A, 1992, 185: 87. Liu De, Li Hou-qiang, et al. Communications in Nolinear Science and Numerical Simulation, 1997, 2: 156. Metzler R, Glokie W G, Nonnenmacher T F. Physica A, 1994, 211: 13. O'Shaughnessy B, Procaccia I. Phys Rev A, 1985, 32: 3073. -
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