Lie Group Classifications and Non-differentiable Solutions for Time-Fractional Burgers Equation

Lie group method provides an efficient tool to solve nonlinear partial differential equations. This paper suggests Lie group method for fractional partial differential equations. A time-fractional Burgers equation is used as an example to illustrate the effectiveness of the Lie group method and some classes of exact solutions are obtained.

杜布瓦雷蒙分型工作的初衷

分型与黎曼函数是杜布瓦雷蒙对线性偏微分方程理论的独特贡献。本文就杜布瓦雷蒙的思想渊源和此二项工作的逻辑关系对原文进行了详细的考查,指出,分型目的在于推广黎曼方法,也是将该方法一般化的必要前提。比起黎曼方法,分型本身在原文作者心目中是次要的。杜布瓦雷蒙之所以能完成分型,一个决定因素是他早年研究过的特征理论。无论偏微分方程理论的发展如何改变分型和黎曼函数的份量,搞清楚杜布瓦雷蒙分型的初衷对于客观评价他的贡献都是必要的。