分形介质分数阶反常守恒扩散模型及其解析解

Fractional anomalous conservation diffusion model and its analytic solution in fractal media

建立了分形介质中分数阶瞬时点源反常守恒扩散模型 .并利用分数阶微积分理论和Fox函数理论给出了解析解 ,同时给出了散射函数谱的表达式 .结果表明 ,散射函数谱仍具有尺度函数的特性 ,经典的瞬时点源扩散问题可作为特例 ,所得解析解可作为基本解进行叠加 .

The model of fractional anomalous diffusion caused by an instantaneous point source in fractal media is established. Using the theories of fraction calculus and H-function, the analytical solutions of concentration distribution are given. At the same time we derive the expressions of scattering function spectrum. The result shows that the scattering function spectra still have the properties of scaling function, classical diffusion problems caused by instantaneous point source can be regarded as particular cases of this paper.