改进的分数阶辅助方程方法及其在非线性空间时间分数阶微分方程中的应用

赵梅妹

doi:10.13718/j.cnki.xsxb.2018.11.005

西南师范大学学报(自然科学版)

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改进的分数阶辅助方程方法及其在非线性空间时间分数阶微分方程中的应用

赵梅妹. 改进的分数阶辅助方程方法及其在非线性空间时间分数阶微分方程中的应用[J]. 西南师范大学学报(自然科学版), 2018, 43(11): 24-29. doi: 10.13718/j.cnki.xsxb.2018.11.005

引用本文:

ZHAO Mei-mei. On Improved Fractional Sub-Equation Method and Its Applications to Nonlinear Space-Time Fractional Equations[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(11): 24-29. doi: 10.13718/j.cnki.xsxb.2018.11.005

Citation:

ZHAO Mei-mei. On Improved Fractional Sub-Equation Method and Its Applications to Nonlinear Space-Time Fractional Equations[J]. Journal of Southwest China Normal University(Natural Science Edition), 2018, 43(11): 24-29. doi: 10.13718/j.cnki.xsxb.2018.11.005

改进的分数阶辅助方程方法及其在非线性空间时间分数阶微分方程中的应用

赵梅妹

西安翻译学院基础科学系, 西安 710105

On Improved Fractional Sub-Equation Method and Its Applications to Nonlinear Space-Time Fractional Equations

ZHAO Mei-mei

Basic Science Department, Engineering and Technology School, Xi'an Fanyi University, Xi'an, 710105, China

摘要: 利用改进的分数阶辅助方程方法求解具有修正的Riemann-Liouville分数阶导数的非线性发展方程组.将该方法应用到空间-时间分数阶Broer-Kaup方程组和空间-时间分数阶长水波近似方程组，并通过符号计算得到这两类方程组的精确行波解.结果表明，该方法能十分有效和便捷地得到时间-空间分数阶非线性微分方程组的解.
- 改进的分数阶辅助方程方法 /
- 修正的Riemann-Liouville分数阶导数 /
- 分数阶微分方程 /
- Broer-Kaup方程组 /
- 长水波近似方程组
Abstract: An improved fractional sub-equation method is applied to solve nonlinear evolution equations involving Jumarie's modified Riemann-Liouville derivative. In this method, the space-time fractional Broer-Kaup and the approximate long water wave equations are considered and exact traveling wave solutions are explicitly obtained with the aid of symbolic computation. As a result, the obtained solutions show that the proposed method is very effective and convenient.
- improved fractional sub-equation method /
- modified Riemann-Liouville derivative /
- fractional differential equation /
- Broer-Kaup equations /
- approximate long water wave equations .

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改进的分数阶辅助方程方法及其在非线性空间时间分数阶微分方程中的应用

赵梅妹

西安翻译学院基础科学系, 西安 710105

收稿日期: 2017-02-23

关键词:

摘要: 利用改进的分数阶辅助方程方法求解具有修正的Riemann-Liouville分数阶导数的非线性发展方程组.将该方法应用到空间-时间分数阶Broer-Kaup方程组和空间-时间分数阶长水波近似方程组，并通过符号计算得到这两类方程组的精确行波解.结果表明，该方法能十分有效和便捷地得到时间-空间分数阶非线性微分方程组的解.