非齐次反常次扩散方程的解析解

Abstract

扩散、对流-扩散和Fokker-Planck型的分数阶动力方程为描述在复杂系统中由反常扩散控制的传送动力学提供实用的近似.利用分离变量方法和Laplace变换分别导出在Dirichlet、Neumann和Robin边界条件下的非齐次反常次扩散方程的解析解.这个技巧可以推广到解其它类型的反常扩散方程.

Fractional kinetic equations of the diffusion,diffusion-advection,and Fokker-Planck type are presented as a useful approach for the description of transport dynamics in complex systems which are governed by anomalous diffusion.The theoretical justification for the fractional diffusion equation,together with the abundance of physical and biological experiments demonstrating the prevalence of anomalous sub-diffusion(ASub-DE),has led to an intensive effort in recent years to find accurate and stable methods of solution that are also straightforward to implement.However,effective methods for the ASub-DE are still in their infancy.In this paper,using separation of variable methods and Laplace transform,the analytical solutions of a non-homogeneous ASub-DE with Dirichlet,Neumann and Robin boundary conditions are derived,respectively.These techniques can be applied to solve other kinds of anomalous diffusion.