分数微分方程的发展和应用

On the Developments and Applications of Fractional Differential Equations

阐述分数微分方程的发展历程、现状和应用背景,提出从推广经典微分方程角度展开研究工作的若干问题与建议.

The main objective of the paper is to give an overview of the developments and applications of fractional differential equations.There are many examples which have shown that new fractional-order models are more adequate than previously used integer-order models.However,the effective generalization for the stability and geometrical theory of ordinary differential equation cannot be found even in the most useful works on fractional differential equations.So the another objective of this paper is to make some appraisals and suggestions for the theory of fractional differential equations,which hopefully conduces to its developments in the future.