一类ψ-Caputo分数阶微分方程解的存在性和Ulam-Hyers稳定性  

Existence and stability of solution for a special Caputo fractional differential equation

作　　者：李晓艳[1] 任玮 谢地 蒋威[1] LI Xiaoyan;REN Wei;XIE Di;JIANG Wei(School of Mathematical Sciences,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《安徽大学学报（自然科学版）》2023年第1期8-16,共9页Journal of Anhui University(Natural Science Edition)

基　　金：安徽省教育厅重点资助项目(KJ2019A0004)。

摘　　要：主要讨论在有限闭区间[a,b]上关于另一个函数的非线性Caputo分数阶微分方程.首先,给出了初值问题解的存在性和唯一性的充分条件.其次,利用Krasnoselskii不动点定理证明了该方程解的存在唯一性.最后,分两种情况讨论了系统的Ulam-Hyers-Rassias稳定性.This paper mainly discussed a nonlinear Caputo fractional differential equation with respect to another function on finite interval a,b.Firstly,sufficient conditions for the existence of solution and uniqueness for the initial value problem were obtained.Then,the existence of solution for the equation was proved by using Krasnoselskii’s fixed point theorem.At last,Ulam-Hyers-Rassias stability of the system was discussed in two forms.

关 键 词：Caputo分数阶微分方程 KRASNOSELSKII不动点定理 Ulam-Hyers稳定性 

分 类 号：O156[理学—数学]