广西师范大学学报（自然科学版） ›› 2023, Vol. 41 ›› Issue (6): 92-104.doi: 10.16088/j.issn.1001-6600.2023032202

• • 上一篇    下一篇

Caputo型分数阶微分系统正解的唯一性

徐紫钰, 吴克晴*   

  1. 江西理工大学 理学院, 江西 赣州 341000
  • 收稿日期:2023-03-22 修回日期:2023-05-08 发布日期:2023-12-04
  • 通讯作者: 吴克晴(1972—), 男, 江西鹰潭人, 江西理工大学副教授, 博士。 E-mail: 317595750@qq.com
  • 基金资助:
    国家自然科学基金(61364015)

Uniqueness of Positive Solutions for Caputo Fractional Differential Systems

XU Ziyu, WU Keqing*   

  1. School of Science, Jiangxi University of Science and Technology, Ganzhou Jiangxi 341000, China
  • Received:2023-03-22 Revised:2023-05-08 Published:2023-12-04

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摘要： 考虑一类非线性p-Laplacian分数阶微分方程耦合系统多点边值问题,其中非线性函数包含Caputo分数阶导数,其边界条件包含非线性积分项。基于和算子的广义不动点定理及分数阶微积分算子的性质,分析该耦合系统的唯一正解;借助相应算子方程推导出唯一正解的存在性;通过数值算例对主要结果进行检验分析。

关键词: 正解, 分数阶导数, 算子方程, p-Laplacian, 唯一性

Abstract: A class of nonlinear p-Laplacian fractional differential equation coupling systems with multipoint boundary value problems is considered where the nonlinear function contains the Caputo fractional derivative and the boundary conditions include nonlinear integral terms. Based on the generalized fixed point theorem of sum operator and the properties of fractional calculus operator, the unique positive solution of the coupling system is analyzed. The existence of the unique positive solution is deduced by means of the corresponding operator equation, and the main results are obtained. The main results are tested by numerical examples.

Key words: positive solution, fractional derivative, operator equation, p-Laplacian, uniqueness

中图分类号:  O175.8

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