Models of the neutral-fractional anomalous diffusion and their analysis
Models of the neutral-fractional anomalous diffusion and their analysis
复制标题
中性分数反常扩散模型及其分析
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Yuri Luchko
中科院分区：
文献类型：
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作者：
Yuri Luchko
异常的扩散可以大致以扩散颗粒不遵循高斯统计的特性来大致特征。当粒子的平均平方位移像功率函数一样，时间和/或空间折叠式衍生物被证明可用于建模此类扩散过程。在本文中，考虑了一类特殊的异常扩散过程，即所谓的中性裂纹扩散。起点是根据连续时间随机步行过程的随机公式。然后以相同顺序和空间中相同顺序的偏微分方程形式的中端扩散方程从主方程中得出，以特殊选择概率密度函数。提出了凯奇问题的基本解决方案的明确形式，以实现中性分流扩散方程。它的特性由图研究和说明。
Anomalous diffusion can be roughly characterized by the property that the diffusive particles do not follow the Gaussian statistics. When the mean squared displacement of the particles behaves in time like a power function, time- and/or space-fractional derivatives were shown to be useful in modeling of such diffusion processes. In this paper, a special class of anomalous diffusion processes, the so called neutral-fractional diffusion, is considered. The starting point is a stochastic formulation of the model in terms of the continuous time random walk processes. The neutralfractional diffusion equation in form of a partial differential equation with the fractional derivatives of the same order both in time and in space is then derived from the master equation for a special choice of the probability density functions. An explicit form of the fundamental solution of the Cauchy problem for the neutral-fractional diffusion equation is presented. Its properties are studied and illustrated by plots.