时间分数阶KdV方程的级数解

Series solutions of the time fractional KdV equations

主要考虑Riemann-Liouville积分和Caputo导数意义下的分数阶KdV方程初值问题,通过一类迭代法构造分数阶KdV方程在实数域上的级数解,并将这类迭代法推广到复空间上,建立了分数阶KdV方程在复数域上的级数解.这类迭代法只依赖于初值的选取,对于非线性分数阶偏微分方程,甚至是耦合系统,都能有效地建立级数解.

The construction of series solution to the KdV equations in the sense of Riemann-Liouville integral and Caputo derivative is considered. For given initial value, by an iterative method,it can be successfully obtained the approximate series solutions of the real and complex KdV equations. By the construction process, it shows the iteration is an efficient method, which can be used to other fractional differential equations and even coupled systems.