| 周碧波,张玲玲.经由和型算子方法下共形分数阶微分方程正解的唯一性和迭代序列[J].数学研究及应用,2022,42(4):349~362 |
| 经由和型算子方法下共形分数阶微分方程正解的唯一性和迭代序列 |
| Uniqueness and Iterative Schemes of Positive Solutions for Conformable Fractional Differential Equations via Sum-Type Operator Method |
| 投稿时间：2021-09-20 修订日期：2022-02-19 |
| DOI：10.3770/j.issn:2095-2651.2022.04.002 |
| 中文关键词: 正解 存在唯一性 共形分数阶导数 和型算子 边值问题 |
| 英文关键词:positive solutions existence-uniqueness conformable fractional derivatives sum-type operator boundary value problems |
| 基金项目:山西省重点研发计划项目(国际合作) (Grant No.201903D421042), 山西省回国留学人员科研资助项目(Grant No.2021-303). |
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| 中文摘要: |
| 本文研究了一类共形分数阶微分方程两点边值问题,通过利用定义在锥上的一类和型算子不定点定理,获得了微分方程正解存在唯一性,并构造一个迭代序列逼近唯一正解.最后,通过两个例子验证了本文获得的主要结论. |
| 英文摘要: |
| We are concerned with two points boundary value problems for a kind of conformable fractional differential equations in this paper. By employing the fixed point theorems for a class of sum-type operator defined on a cone, the existence-uniqueness and iterative schemes converging to unique positive solution are established. As applications, two examples are presented to illustrate our main results. |
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