求解非线性分数阶偏微分方程精确解的几种方法  

Several Methods for Solving the Exact Solutions of Nonlinear Fractional Partial Differential Equations

作　　者：张慧 ZHANG Hui(School of General Education,City College,Southwest University of Science and Technology,Mianyang 621000,China)

机构地区：[1]西南科技大学城市学院通识教育学院,四川绵阳621000

出　　处：《湖北民族大学学报（自然科学版）》2020年第3期313-317,共5页Journal of Hubei Minzu University:Natural Science Edition

基　　金：重庆市科委项目(cstc2018jcyjAX0766).

摘　　要：最近几十年,越来越多的求解分数阶微分方程的有效方法被提出来,然而这些方法各有利弊.本文介绍了3种不同的方法计算非线性分数阶偏微分方程的精确解,并比较了3种方法的利弊.利用不变子空间法、变量分离与齐次平衡原理相结合的方法、齐次平衡与积分分支相结合的方法分别求解时间分数阶扩散-对流微分方程,得到了该方程的各类精确解,这些精确解包括参数形式的解、周期形式的解和幂函数形式的解、椭圆积分函数形式的解.In recent decades,more and more effective methods to solve fractional differential equations have been proposed,but these methods have their own advantages and disadvantages.In this paper,we introduce three different methods to solve the exact solution of the nonlinear fractional partial differential equation,and compare the advantages and disadvantages of the three methods.By using the invariant subspace method,the method of variable separation and homogeneous balance principle,the method of homogeneous balance and integral bifurcation to solve the time fractional diffusion convection differential equation,and different kinds of exact solutions of them are obtained.These exact solutions include parametric type solutions,periodic type solutions,power function type solutions and elliptic integral function type solutions.

关 键 词：齐次平衡法 变量分离法 精确解 不变子空间 积分分支 

分 类 号：O29[理学—应用数学]