一个时间分数阶扩散方程的精确解和动力学性质  

Exact Solution and Dynamical Properties of a Time-fractional Diffusion Equation

作　　者：黎超玲 赵云梅 LI Chao-ling;ZHAO Yun-mei(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China;College of Mathematics and Statistics,Honghe University,Mengzi 661199,Yunnan,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]红河学院数学与统计学院,云南蒙自661199

出　　处：《红河学院学报》2023年第5期133-137,共5页Journal of Honghe University

基　　金：重庆市科委基础研究与前沿探索专项项目(cstc2018jcyjAX0766)。

摘　　要：众所周知,相比于整数阶非线性偏微分方程的求解问题,分数阶非线性偏微分的精确求解问题是一个极为困难的问题.文章利用半固定式变量分离方法与动力系统方法相结合的方式,研究了一个时间分数阶扩散方程的精确解及其动力学性质.获得了比原始文献中得到的精确解更加丰富的内容,并讨论了部分新精确解的动力学性质,通过解的坐标演化图直观地展示了在不同参数条件下的扩散现象.It is well known that the exact problem of solving fractional nonlinear partial differential equations is a very difficult problem compared with those of integer-order nonlinear partial differential equations.In this paper,we study the exact solution of a time-fractional diffusion equation and its dynamical properties by using a semi-fixed variable separation approach combined with a dynamical system method.Some richer contents than those obtained in the original literature and discuss their dynamical properties of some new exact solutions,visually showing the diffusion phenomenon under different parameters through the graphs of coordinate evolution for some solutions.

关 键 词：时间分数阶扩散方程 Riemann-Liouville分数阶导数 半固定式变量分离法 动力系统方法 精确解 

分 类 号：O175.08[理学—数学]