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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (8): 82-91.doi: 10.6040/j.issn.1671-9352.0.2023.034

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适型分数阶耦合系统正解的存在性和Ulam稳定性

倪云(),刘锡平#()   

  1. 上海理工大学理学院, 上海 200093
  • 收稿日期:2023-02-01 出版日期:2023-08-20 发布日期:2023-07-28
  • 通讯作者: 刘锡平 E-mail:nyny0418_h@163.com;xipingliu@usst.edu.cn
  • 作者简介:倪云(1998—), 女, 硕士研究生, 研究方向为常微分方程理论与应用研究. E-mail: nyny0418_h@163.com
  • 基金资助:
    上海市“科技创新行动计划”启明星培育(扬帆专项)项目(23YF1429100)

Existence and Ulam stability for positive solutions of conformable fractional coupled systems

Yun NI(),Xiping LIU#()   

  1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
  • Received:2023-02-01 Online:2023-08-20 Published:2023-07-28
  • Contact: Xiping LIU E-mail:nyny0418_h@163.com;xipingliu@usst.edu.cn

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摘要：

研究了一类带p-Laplace算子的适型分数阶微分方程耦合系统非局部边值问题。首先, 通过构造一个特殊的Banach空间, 利用Schauder不动点定理和Banach压缩映射原理得到了系统正解的存在性与唯一性等多个结论, 给出了系统正解存在及唯一的充分条件。然后, 重点研究了系统的稳定性, 得到了系统具有广义Hyers-Ulam稳定性的结论。最后, 通过具体事例说明所得主要结论的适用性。

关键词: 适型分数阶导数, 耦合系统, p-Laplace算子, 非局部边值问题, Hyers-Ulam稳定性

Abstract:

A nonlocal boundary value problem for a class of conformable fractional differential equations coupled system with p-Laplacian operator are studied. First, by constructing a special Banach space and using the Schauder fixed-point theorem and Banach contraction mapping principle, several results on the existence and uniqueness for positive solutions to the system are obtained, and provide sufficient conditions for the existence and uniqueness of the solution. Then, the stability of the system is studied, and the conclusion that the system has the generalized Hyers-Ulam stability is obtained. Finally, the applicability of the main conclusions obtained is demonstrated through a specific example.

Key words: conformable fractional derivative, coupled system, p-Laplacian operator, nonlocal boundary value problem, Hyers-Ulam stability

中图分类号: 

  • O175.8
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