一类Caputo-Katugampola型分数阶微分方程耦合系统边值问题

doi:10.13438/j.cnki.jdzk.2024.05.003

吉首大学学报（自然科学版） ›› 2024, Vol. 45 ›› Issue (5): 17-27.DOI: 10.13438/j.cnki.jdzk.2024.05.003

一类Caputo-Katugampola型分数阶微分方程耦合系统边值问题

黎宁静，何小飞，陈国平

(吉首大学数学与统计学院，湖南吉首 416000)

出版日期:2024-09-25 发布日期:2024-11-08
通讯作者: 何小飞(1971—),男,湖南新邵人,吉首大学数学与统计学院教授,博士,主要从事微分方程与动力系统研究.
作者简介:黎宁静(2000—),女,湖南醴陵人,吉首大学数学与统计学院硕士研究生,主要从事微分方程与动力系统研究

Boundary Value Problems for a Class of Coupled System of Caputo-Katugampola Type Fractional Differential Equation

LI Ningjing,HE Xiaofei,CHEN Guoping

(College of Mathematics and Statistics,Jishou University,Jishou 416000,Hunan China)

Online:2024-09-25 Published:2024-11-08

摘要/Abstract

摘要：利用Leray-Schauder二择一定理和Schauder不动点定理，研究了一类具有Caputo-Katugampola型导数的分数阶微分方程耦合系统边值问题解的存在唯一性,再利用Banach不动点定理和Ulam-Hyers稳定性的定义，讨论了该边值问题的Ulam-Hyers稳定性.

关键词： 分数阶微分方程, Caputo-Katugampola型导数, 耦合系统, 不动点定理, Ulam-Hyers稳定性

Abstract: In this paper,by using Leray-Schauder alternative theorem and Schauder fixed point theorem,we study the existence and uniqueness of solutions of boundary value problems for a class of fractional differential equations coupled systems with Caputo-Katugampola derivatives,and study the Ulam-Hyers stability of the boundary value problems by using Banach fixed point theorem and the definition of Ulam-Hyers stability.

Key words: fractional differential equation, Caputo-Katugampola derivative, coupled system, fixed point theorem, Ulam-Hyers stability

黎宁静, 何小飞, 陈国平. 一类Caputo-Katugampola型分数阶微分方程耦合系统边值问题[J]. 吉首大学学报（自然科学版）, 2024, 45(5): 17-27.

LI Ningjing, HE Xiaofei, CHEN Guoping. Boundary Value Problems for a Class of Coupled System of Caputo-Katugampola Type Fractional Differential Equation [J]. Journal of Jishou University(Natural Sciences Edition), 2024, 45(5): 17-27.

参考文献

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一类Caputo-Katugampola型分数阶微分方程耦合系统边值问题

Boundary Value Problems for a Class of Coupled System of Caputo-Katugampola Type Fractional Differential Equation

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