时间分数阶KdV方程的级数解  

Series solutions of the time fractional KdV equations

作　　者：高忆先[1] 李金玉[1] 徐飞[1] 

机构地区：[1]东北师范大学数学与统计学院,吉林长春130024

出　　处：《东北师大学报（自然科学版）》2017年第2期1-5,共5页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11471067);吉林省科技发展计划资助项目(20160520094JH)

摘　　要：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.

关 键 词：时间分数阶KdV方程 Riemann-Liouville积分 CAPUTO导数 迭代法 级数解 

分 类 号：O193[理学—数学]