| 张海燕,李耀红.无穷区间上一类分数阶微分方程正解的显式迭代序列[J].数学研究及应用,2020,40(1):13~25 |
| 无穷区间上一类分数阶微分方程正解的显式迭代序列 |
| Explicit Iterative Sequences of Positive Solutions for a Class of Fractional Differential Equations on an Infinite Interval |
| 投稿时间：2018-10-17 修订日期：2019-04-11 |
| DOI：10.3770/j.issn:2095-2651.2020.01.002 |
| 中文关键词: 单调迭代技巧 迭代序列 分数阶微分方程 无穷区间 |
| 英文关键词:monotone iterative method iterative sequences fractional differential equations infinite interval |
| 基金项目:安徽省高校自然科学基金重点项目(Grant Nos.KJ2017A442; KJ2018A0452; KJ2019A0666), 宿州学院基金(Grant Nos.2016XJGG13; 2019XJZY02; 2019XJSN03). |
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| 中文摘要: |
| 通过应用单调迭代技巧,本文获得了两个逼近极小和极大正解的显式迭代序列.同时,通过应用Banach压缩不动点定理,一个逼近唯一正解的显式迭代序列和误差估计被获得.并给出若干例子说明结果的应用性. |
| 英文摘要: |
| By applying the monotone iterative method, this study develops two explicit monotone iterative sequences for approximating the minimal and maximal positive solutions. At the same time, by applying the Banach fixed-point theory, an explicit iterative sequence and error estimate for approximating the unique positive solution is obtained. Some examples are given to illustrate the application of the results. |
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