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

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

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.

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.