时间分数阶DP方程的精确解及其动力学性质研究  

Exact Solution and Dynamical Properties of The Time-fractional DP Equation

作　　者：邹静 何应辉 张宏杰 ZOU Jing;HE Ying-hui;ZHANG Hong-jie(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China;School of Mathematics&Statistics,Honghe University,Mengzi 661199,Yunnan,China;School of Basic Education,Chongqing Industry&Trade Polytechnic,Fuling of Chongqing 408000,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 [3]重庆工贸职业技术学院基础教育学院,重庆408000

出　　处：《红河学院学报》2025年第2期126-131,共6页Journal of Honghe University

基　　金：云南省高校联合面上项目(2018FH001-013);重庆工贸职业技术学院校级科研项目(ZR202314)。

摘　　要：在分数阶微分方程研究领域,要想获得非线性分数阶偏微分方程的精确解是一件十分困难的事情.利用半固定式变量分离法与平面分支法相结合的组合算法,分别在两种经典的分数阶算子下,系统地研究了时间分数阶Degasperis-Procesi方程的精确解,在某些参数条件下获得了这类方程的各种精确解,进一步讨论了解的动力学性质,通过解的三维坐标演化图直观地展示了一些解的动力学行为.In the research field of fractional differential equations,trying to obtain exact solutions of a nonlinear fractional PDEs is a very difficult work.By using separation method of semi-fixed variables and plane bifurcation method,exact solutions of time-fractional Degasperis-Procesi equation are investigated under two kinds of fractional differential operators.In some parametric conditions,different kinds of exact solutions are obtained,and their dynamical properties are further discussed.And their dynamic properties are analyzed by the graphs of these solutions under different parameters.

关 键 词：时间分数阶 DEGASPERIS-PROCESI方程 半固定式变量分离法 平面分支法 

分 类 号：O175.2[理学—数学]