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

Shuyi Wang and Fanwei Meng
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Shuyi Wang: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
Fanwei Meng: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Mathematics, 2021, vol. 9, issue 23, 1-17

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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