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Volume 9
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Article

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

by
Shuyi Wang
* and
Fanwei Meng
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
*
Author to whom correspondence should be addressed.
Mathematics 2021, 9(23), 3029; https://doi.org/10.3390/math9233029
Submission received: 20 October 2021 / Revised: 18 November 2021 / Accepted: 19 November 2021 / Published: 26 November 2021
(This article belongs to the Special Issue Advances in Delay Differential Equations)
Versions Notes

Abstract

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.
Keywords: Ulam stability; delay integro-differential equation; Gronwall–Bellman inequality Ulam stability; delay integro-differential equation; Gronwall–Bellman inequality

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MDPI and ACS Style

Wang, S.; Meng, F. Ulam Stability of n-th Order Delay Integro-Differential Equations. Mathematics 2021, 9, 3029. https://doi.org/10.3390/math9233029

AMA Style

Wang S, Meng F. Ulam Stability of n-th Order Delay Integro-Differential Equations. Mathematics. 2021; 9(23):3029. https://doi.org/10.3390/math9233029

Chicago/Turabian Style

Wang, Shuyi, and Fanwei Meng. 2021. "Ulam Stability of n-th Order Delay Integro-Differential Equations" Mathematics 9, no. 23: 3029. https://doi.org/10.3390/math9233029

APA Style

Wang, S., & Meng, F. (2021). Ulam Stability of n-th Order Delay Integro-Differential Equations. Mathematics, 9(23), 3029. https://doi.org/10.3390/math9233029

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