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New Fundamental Results on the Continuous and Discrete Integro-Differential Equations

Author

Listed:
  • Osman Tunç

    (Department of Computer Programing, Baskale Vocational School, Van Yuzuncu Yil University, Van 65080, Turkey
    These authors contributed equally to this work.)

  • Cemil Tunç

    (Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van 65080, Turkey
    These authors contributed equally to this work.)

  • Jen-Chih Yao

    (Research Center for Interneural Computing, China Medical University Hospital, China Medical University, Taichung 404332, Taiwan)

  • Ching-Feng Wen

    (Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 80708, Taiwan
    Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 80708, Taiwan)

Abstract

This work studies certain perturbed and un-perturbed nonlinear systems of continuous and discrete integro-delay differential equations (IDDEs). Using the Lyapunov–Krasovskii functional (LKF) method and the Lyapunov–Razumikhin method (LRM), uniform asymptotic stability (UAS), uniform stability (US), integrability and boundedness of solutions as well as exponential stability (ES) and instability of solutions are discussed. In this paper, five new theorems and a corollary are given and three numerical applications are provided with their simulations. With this work, we aim to make new contributions to the theory of the continuous and discrete integro-differential equations.

Suggested Citation

  • Osman Tunç & Cemil Tunç & Jen-Chih Yao & Ching-Feng Wen, 2022. "New Fundamental Results on the Continuous and Discrete Integro-Differential Equations," Mathematics, MDPI, vol. 10(9), pages 1-18, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1377-:d:797979
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    Cited by:

    1. Boykov, I.V. & Roudnev, V.A. & Boykova, A.I., 2024. "Stability of solutions of systems of Volterra integral equations," Applied Mathematics and Computation, Elsevier, vol. 475(C).

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