时间分数阶Gardner方程的新精确解  

New Exact Solutions for the Time Fractional Gardner Equation

作　　者：黄春[1] HUANG Chun(Dept.of Teachers Education,Sichuan Vocational and Technical College,Suining,Sichuan Province 629000)

机构地区：[1]四川职业技术学院教师教育系,四川遂宁629000

出　　处：《楚雄师范学院学报》2020年第6期17-22,共6页Journal of Chuxiong Normal University

基　　金：四川省教育厅科研项目(NO.18ZB0537)。

摘　　要：首先利用分数阶复变换和修正的Riemann-Liouville分数阶导数将非线性分数阶偏微分方程转化为整数阶常微分方程,然后基于首次积分法得到时间分数阶Gardner方程的新精确解,其中包括双曲函数解、孤立波解、有理函数解,丰富了其精确解解系。该方法简洁高效可应用于构建其他类型分数阶偏微分方程的精确解。By using the complex transform and modified Riemann-Liouville fractional derivative,the nonlinear fractional-order partial differential equation is converted to an ordinary integer-order differential equation.Then,the first integral method is used to construct new exact solutions for time fractional Gardner equation.The obtained exact solutions include hyperbolic function solutions,solitary wave solutions and rational function solutions,enriching the exact solution family of the equation.This method is efficient and powerful for solving other types of fractional differential equations.

关 键 词：时间分数阶Gardner方程 Riemann-Liouville导数 首次积分法 精确解 

分 类 号：O175.2[理学—数学]