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

Author

Listed:
  • Shuyi Wang

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

  • Fanwei Meng

    (School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

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.

Suggested Citation

  • Shuyi Wang & Fanwei Meng, 2021. "Ulam Stability of n -th Order Delay Integro-Differential Equations," Mathematics, MDPI, vol. 9(23), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3029-:d:688451
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    References listed on IDEAS

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    1. Liu, Kui & Wang, JinRong & Zhou, Yong & O’Regan, Donal, 2020. "Hyers–Ulam stability and existence of solutions for fractional differential equations with Mittag–Leffler kernel," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    2. Zada, Akbar & Ali, Wajid & Park, Choonkil, 2019. "Ulam’s type stability of higher order nonlinear delay differential equations via integral inequality of Grönwall-Bellman-Bihari’s type," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 60-65.
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