分数阶Feller算子下的反常扩散方程

The Anomalous Diffusion Equation with Fractional Feller’s Operator

建立了Feller算子Dθα下的空间分数阶反常扩散方程,给出分数阶扩散方程Canchy问题的求解定理,借助定理、Fourier变换及伽利略变换不变性得到问题的精确解,并当α→2即θ→0时,问题的解与相应经典整数阶扩散(对流–扩散)方程的解一致.

The author discusses the anomalous diffusion equation with fractional Feller＇s operator, and gets it＇s analytical solution by means of Fourier transform. When α→2,θ→0, the analytical solution just coincides with that of the classical diffusion （advection -diffusion） equation.