(3+1)维时空分数阶mKdV-ZK方程的精确解

The exact solutions of the (3+1)-dimensional space-time fractional mKdV-ZK equation

借助一个分数阶子方程和修正的Riemann-Liouville分数阶导数,基于扩展的(G′/G)-展开法,介绍了求解分数阶微分方程精确解的一种新方法,并利用该方法求解了(3+1)维时空分数阶mKdV-ZK方程,获得了该方程用双曲函数和三角函数等表示的精确解.

By means of a fractional sub-equation and the modified Riemann-Liouville fractional derivative, based on the extended （G＇/G）-extended expansion method, a new method is solutions of fractional differential equation. To illustrate the effectiveness of the method, （3 ＋ 1）- dimensional space-time fractional mKdV ZK equation is discussed, many types of exact solutions are obtained, these solutions include hyperbolic function, trigonometric and so on.