| 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 |
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| 引用本文： | 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 |
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| 作者姓名： | 周碧波 张玲玲 |
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| 作者单位： | 太原理工大学数学学院, 山西 太原 030024; 吕梁学院数学系, 山西 吕梁 033000 |
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| 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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| 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.
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| 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 |
| 收稿时间： | 2021-09-20 |
| 修稿时间： | 2022-02-19 |
Uniqueness and Iterative Schemes of Positive Solutions for Conformable Fractional Differential Equations via Sum-Type Operator Method |
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| Bibo ZHOU,Lingling ZHANG. Uniqueness and Iterative Schemes of Positive Solutions for Conformable Fractional Differential Equations via Sum-Type Operator Method[J]. Journal of Mathematical Research with Applications, 2022, 42(4): 349-362 |
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| Authors: | Bibo ZHOU Lingling ZHANG |
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| Affiliation: | College of Mathematics, Taiyuan University of Technology, Shanxi 030024, P. R. China; Department of Mathematics, Lyuliang University, Shanxi 033000, P. R. China |
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| Abstract: | 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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| Keywords: | positive solutions existence-uniqueness conformable fractional derivatives sum-type operator boundary value problems |
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