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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (4): 53-61.doi: 10.6040/j.issn.1671-9352.0.2022.565

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一类具有Hadamard导数的分数阶微分方程积分边值问题正解的存在唯一性

胡芳芳1,2(),胡卫敏1,2,*(),张永1,2   

  1. 1. 伊犁师范大学数学与统计学院, 新疆 伊宁 835000
    2. 伊犁师范大学应用数学研究所, 新疆 伊宁 835000
  • 收稿日期:2022-10-31 出版日期:2024-04-20 发布日期:2024-04-12
  • 通讯作者: 胡卫敏 E-mail:1594664266@qq.com;hwm680702@163.com
  • 作者简介:胡芳芳(1994—), 女, 讲师, 硕士, 研究方向为微分方程理论与应用. E-mail: 1594664266@qq.com
  • 基金资助:
    伊犁师范大学校级资助项目(2023YSYB010);伊犁州科技计划资助项目(YZ2022Y013);伊犁师范大学科研创新团队资助项目(CXZK2021016)

Existence and uniqueness of positive solutions of integral boundary value problems for a class of fractional differential equations with Hadamard derivatives

Fangfang HU1,2(),Weimin HU1,2,*(),Yong ZHANG1,2   

  1. 1. College of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang, China
    2. Institute of Applied Mathematics, Yili Normal University, Yining 835000, Xinjiang, China
  • Received:2022-10-31 Online:2024-04-20 Published:2024-04-12
  • Contact: Weimin HU E-mail:1594664266@qq.com;hwm680702@163.com

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摘要：

研究一类具有积分边值条件的Hadamard分数阶微分方程边值问题, 利用Schauder不动点定理和上下解方法得到正解的存在性, 通过Banach压缩映射原理得到唯一性结果, 并给出实例说明结果的有效性。

关键词: Hadamard分数阶导数, 分数阶微分方程, 不动点定理, 存在唯一性

Abstract:

A class of boundary value problems for Hadamard fractional differential equations with integral boundary value conditions is studied. The existence of positive solutions is obtained by Schauder fixed point theorem and the upper and lower solution method. The uniqueness result is obtained by Banach compression mapping principle, and an example is given to illustrate the effectiveness of the results.

Key words: Hadamard fractional derivative, fractional differential equation, fixed point theorem, existence and uniqueness

中图分类号: 

  • O175.14
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