空间—时间分数阶对流扩散方程的分析解及基本解的性质

The Analytic Solution and the Fundamental Solution of a Space and Time Fractional Advection-dispersion Equation

本文考虑空间时间分数阶对流—扩散方程(即在一个标准对流—扩散方程中,用β(0<β≤1)阶导数代替时间一阶导数,用a(1<a≤2)阶导数代替空间二阶导数,用γ(0<γ≤1)阶导数代替空间二阶导数的分析解,通过Fourier变换,Laplace变换以及其逆变换等方法求得方程的分析解,并对其基本解进行讨论。

The analytic solution of a space and time fractional advection -dispersion equation is considered. This equation is obtained from an advection -dispersion equation by replacing the second order derivative in space by order derivate in space of order, the first order derivative in space by order derivative in space of order and the first order derivative at time by order derivative at time of order. Using the Fourier transform, the Laplace transform and their inverse transforms, the analytic solution of this equation can be arrived at. The fundamental solution of this equation is discussed.