应用（G’/G2）-展开法求解非线性分数阶微分方程

doi:10.13371/j.cnki.chin.q.j.m.2017.03.005

数学季刊 ›› 2017, Vol. 32 ›› Issue (3): 261-270.doi: 10.13371/j.cnki.chin.q.j.m.2017.03.005

应用（G^’/G²）-展开法求解非线性分数阶微分方程

College of Mathematics, Inner Mongolia University for Nationalities

收稿日期:2015-12-23 出版日期:2017-09-30 发布日期:2020-10-22
作者简介:KANG Zhou-zheng(1985-), male, native of Yichun, Heilongjiang, a lecturer of Inner Mongolia University for Nationalities, M.S.D., engages in nonlinear partial di®erential equations.
基金资助:
Supported by the National Natural Science Foundation of China(11462019)； Supported by the Scientific Research Foundation of Inner Mongolia University for Nationalities(NMDYB1750,NMDGP1713)；

Applications of （G^’/G²）-expansion Method in Solving Nonlinear Fractional Differential Equations

College of Mathematics, Inner Mongolia University for Nationalities

Received:2015-12-23 Online:2017-09-30 Published:2020-10-22
About author:KANG Zhou-zheng(1985-), male, native of Yichun, Heilongjiang, a lecturer of Inner Mongolia University for Nationalities, M.S.D., engages in nonlinear partial di®erential equations.
Supported by:
Supported by the National Natural Science Foundation of China(11462019)； Supported by the Scientific Research Foundation of Inner Mongolia University for Nationalities(NMDYB1750,NMDGP1713)；

摘要/Abstract

摘要： In the current paper, based on fractional complex transformation, the GG2-expansion method which is used to solve differential equations of integer order is developed for finding exact solutions of nonlinear fractional differential equations with Jumarie’s modified Riemann-Liouville derivative. And then, time-fractional Burgers equation and space-fractional coupled Konopelchenko-Dubrovsky equations are provided to show that this method is effective in solving nonlinear fractional differential equations.

关键词: time-fractional Burgers equation, space-fractional coupled Konopelchenko- Dubrovsky equations, exact solutions

Abstract: In the current paper, based on fractional complex transformation, the GG2-expansion method which is used to solve differential equations of integer order is developed for finding exact solutions of nonlinear fractional differential equations with Jumarie’s modified Riemann-Liouville derivative. And then, time-fractional Burgers equation and space-fractional coupled Konopelchenko-Dubrovsky equations are provided to show that this method is effective in solving nonlinear fractional differential equations.

Key words: time-fractional Burgers equation, space-fractional coupled Konopelchenko- Dubrovsky equations, exact solutions

中图分类号:

O175

康周正. 应用（G^’/G²）-展开法求解非线性分数阶微分方程[J]. 数学季刊, 2017, 32(3): 261-270.

KANG Zhou-zheng. Applications of （G^’/G²）-expansion Method in Solving Nonlinear Fractional Differential Equations[J]. Chinese Quarterly Journal of Mathematics, 2017, 32(3): 261-270.

应用（G^’/G²）-展开法求解非线性分数阶微分方程

Applications of （G^’/G²）-expansion Method in Solving Nonlinear Fractional Differential Equations

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