一类分数阶时滞微分方程解的存在性及稳定性  

Existence and stability of solutions for a class of fractional delay differential equations

作　　者：管重阳 董琪翔[1] GUAN Chongyang;DONG Qixiang(School of Mathematical Sciences,Yangzhou University,Yangzhou 225002,China)

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《扬州大学学报（自然科学版）》2023年第3期5-10,20,共7页Journal of Yangzhou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11871064).

摘　　要：利用Banach不动点定理和Leray-Schauder不动点定理,研究一类具有无穷时滞变系数线性分数阶微分方程的解,得到该分数阶微分方程解的存在性和唯一性,并通过Gronwall不等式探讨了该分数阶微分方程的Hyers-Ulam稳定性.By using the Banach fixed point theorem and Leray-Schauder fixed point theorem,the existence and uniqueness of a class of linear fractional differential equations with variable coefficients and infinite delay are obtained.Besides,by means of a class of Gronwall inequalities,the Hyers-Ulam stability of this fractional differential equation is discussed.

关 键 词：分数阶微分方程 无穷时滞 不动点定理 稳定性 

分 类 号：O175.15[理学—数学]