Ulam Stability of n-th Order Delay Integro-Differential Equations

Mathematics

卷:9

Fanwei Meng¹  Shuyi Wang¹ 

[1] School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China;

关键词: Ulam stability;    delay integro-differential equation;    Gronwall–Bellman inequality;   

DOI  :  10.3390/math9233029

来源: DOAJ

【 摘 要 】

In this paper, the Ulam stability of an n-th order delay integro-differential equation is given. Firstly, the existence and uniqueness theorem of a solution for the delay integro-differential equation is obtained using a Lipschitz condition and the Banach contraction principle. Then, the expression of the solution for delay integro-differential equation is derived by mathematical induction. On this basis, we obtain the Ulam stability of the delay integro-differential equation via Gronwall–Bellman inequality. Finally, two examples of delay integro-differential equations are given to explain our main results.

【 授权许可】

Unknown