From continuous time random walks to the generalized diffusion equation
From continuous time random walks to the generalized diffusion equation
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DOI：
10.1515/fca-2018-0002
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发表时间：
2018-02
影响因子：
3
通讯作者：
Trifce Sandev;R. Metzler;A. Chechkin
中科院分区：
文献类型：
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作者：
Trifce Sandev;R. Metzler;A. Chechkin
摘要从连续时间随机游动理论出发，得到了一个修正形式或Riemann-Liouville形式的广义扩散方程。明确计算了不同形式方程的等待时间概率密度函数和均方位移。我们显示的例子，在正常或Caputo形式的广义扩散方程的编码相同的概率分布函数从广义扩散方程的修改形式。所得到的方程是一般的，并包括许多已知的分数阶扩散方程作为特殊情况。
Abstract We obtain a generalized diffusion equation in modified or Riemann-Liouville form from continuous time random walk theory. The waiting time probability density function and mean squared displacement for different forms of the equation are explicitly calculated. We show examples of generalized diffusion equations in normal or Caputo form that encode the same probability distribution functions as those obtained from the generalized diffusion equation in modified form. The obtained equations are general and many known fractional diffusion equations are included as special cases.