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分数阶微分差分方程解的存在性与唯一性

发表时间:2016-01-15  浏览量:1938  下载量:633
全部作者: 孙宇锋,王兆顺,曾广钊,屈威
作者单位: 韶关学院数学与统计学院
摘 要: 从一类分数阶微分差分方程边值问题的近似解出发,应用Picard’s 迭代方法研究证明其边值问题解的迭代序列所满足的形式及其存在唯一解的充要条件;讨论这类边值问题不考虑近似解及非Lipschitz类因素时,其一般解的存在条件;最后通过一个数值算例验证这类边值问题解的存在性以及解与其迭代序列的误差估计。
关 键 词: 常微分方程;分数阶;迭代算法;近似解;误差估计
Title: Existence and uniqueness of solutions for fractional order differential difference equations
Author: SUN Yufeng, WANG Zhaoshun, ZENG Guangzhao, QU Wei
Organization: School of Mathematics and Statistics, Shaoguan University
Abstract: From a class of fractional order differential difference equation boundary value problem of approximate solution, the application Picard’s iteration method is used to prove the form of the boundary problems satisfied by the iterative sequence of the solutions and the necessary and sufficient conditions proving the existence and uniqueness of the solution are discussed. Without considering approximate solution and non Lipschitz class factors, the conditions for the existence of the general solutions of the boundary value problem are discussed. Finally, a numerical example shows the existence of this kind of solution for boundary value problem and the error estimation of the iterative sequence.
Key words: ordinary differential equation; fractional order; iterative algorithm; approximate solution; estimation of error
发表期数: 2016年1月第1期
引用格式: 孙宇锋,王兆顺,曾广钊,等. 分数阶微分差分方程解的存在性与唯一性[J]. 中国科技论文在线精品论文,2016,9(1):55-62.
 
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