分数阶反常扩散方程及其精确解  

Fractional Anomalous Diffusion Equatioan And Its Solution

作　　者：吕龙进[1] 肖建斌[1] 

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2008年第4期92-95,共4页Journal of Hangzhou Dianzi University：Natural Sciences

摘　　要：该文先利用拉普拉斯变换及其逆变换方法求解了一类分数阶反常扩散方程在有限区间上满足吸收边界条件和一般初始条件下的精确解,并且对几类特殊的初始条件求得了方程精确解的具体表达式,接着对所得的结果进一步推广,证明了在有限区间上所得的结果在半无限区间上仍旧适用。In this paper, firstly, we use Laplace transform method to get the exact solution of a fractional anomalous diffusion equation which satisfies to the absorbing boundary condition and the general initial condition on a finite interval. And we get the expressions of solution for some special initial conditions. Then we also analyze this result by extending it to a semi - infinite interval, and we prove that the result got from a finite interval is fit for the semi - infinite interval.

关 键 词：分数次导数 扩散方程 拉普拉斯变换 

分 类 号：O15[理学—数学]