一个非线性分数微分方程奇异解的存在性与逐次迭代方法

数学物理学报 ›› 2016, Vol. 36 ›› Issue (2): 287-296.

一个非线性分数微分方程奇异解的存在性与逐次迭代方法

姚庆六

南京财经大学应用数学系南京 210003

收稿日期:2015-09-17 修回日期:2016-01-26 出版日期:2016-04-25 发布日期:2016-04-25
通讯作者: 姚庆六,yaoqingliu2002@hotmail.com E-mail:yaoqingliu2002@hotmail.com

Existence and Successively Iterative Method of Singular Solution to a Nonlinear Fractional Differential Equation

Yao Qingliu

Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003

Received:2015-09-17 Revised:2016-01-26 Online:2016-04-25 Published:2016-04-25

摘要/Abstract

摘要：

研究了非线性分数微分方程D^αu(t)=f(t,u(t)),0≤t≤1,t^1-αu(t)|_t=0=c解的存在性与迭代方法,其中0< α< 1.当c≠0时该方程的解是奇异的.通过构造了两个在Banach空间C_α[0,1]中收敛于解的逐次迭代序列证明了解的存在性.这项工作改进了文献[8]的主要结论.

关键词: 非线性分数微分方程, 单调迭代方法, 存在性, 收敛速度

Abstract:

The existence and the iterative method of solutions are studied for the nonlinear fractional differential equation D^αu(t)=f(t, u(t)), 0≤t≤1, t^1-αu(t)|_t=0=c, where 0< α< 1. The solutions of the equation are singular if c≠0. By constructing two successively iterative sequences which converge to the solutions in the Banach space C_α[0, 1], the existence of solutions is proved. The main result in [8] is improved by this work.

Key words: Nonlinear fractional differential equation, Monotone iterative method, Existence, Convergence rate

中图分类号:

O175.8

姚庆六. 一个非线性分数微分方程奇异解的存在性与逐次迭代方法[J]. 数学物理学报, 2016, 36(2): 287-296.

Yao Qingliu. Existence and Successively Iterative Method of Singular Solution to a Nonlinear Fractional Differential Equation[J]. Acta mathematica scientia,Series A, 2016, 36(2): 287-296.

参考文献

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