时间分数阶Gardner方程的新精确解

楚雄师范学院学报 ›› 2020, Vol. 35 ›› Issue (6): 17-22.

时间分数阶Gardner方程的新精确解

黄春

四川职业技术学院教师教育系,四川遂宁 629000

收稿日期:2020-05-13 出版日期:2020-11-20 发布日期:2021-03-29
作者简介:黄春（1986–）,女,硕士,四川职业技术学院教师教育系助教,主要研究方向为偏微分方程精确解理论。E-mail：81977889@qq.com,Tel.13699459213
基金资助:
四川省教育厅科研项目（NO.18ZB0537）

New Exact Solutions for the Time Fractional Gardner Equation

HUANG Chun

Dept. of Teachers Education, Sichuan Vocational and Technical College, Suining, Sichuan Province 629000

Received:2020-05-13 Online:2020-11-20 Published:2021-03-29

摘要/Abstract

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。

关键词: 时间分数阶Gardner方程, Riemann-Liouville导数, 首次积分法, 精确解

Abstract: 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.

Key words: time fractional Gardner equation, Riemann-Liouville derivative, first integral method, exact solution

中图分类号:

O175.2

黄春. 时间分数阶Gardner方程的新精确解[J]. 楚雄师范学院学报, 2020, 35(6): 17-22.

HUANG Chun. New Exact Solutions for the Time Fractional Gardner Equation[J]. Journal of Chuxiong Normal University, 2020, 35(6): 17-22.

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