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On Hyers–Ulam and Hyers–Ulam–Rassias Stability of a Nonlinear Second-Order Dynamic Equation on Time Scales

Author

Listed:
  • Alaa E. Hamza

    (Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt
    Department of Mathematics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabia)

  • Maryam A. Alghamdi

    (Department of Mathematics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabia)

  • Mymonah S. Alharbi

    (Department of Mathematics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabia)

Abstract

In this paper, we obtain sufficient conditions for Hyers–Ulam and Hyers–Ulam–Rassias stability of an abstract second–order nonlinear dynamic equation on bounded time scales. An illustrative example is given to show the applicability of the theoretical results.

Suggested Citation

  • Alaa E. Hamza & Maryam A. Alghamdi & Mymonah S. Alharbi, 2021. "On Hyers–Ulam and Hyers–Ulam–Rassias Stability of a Nonlinear Second-Order Dynamic Equation on Time Scales," Mathematics, MDPI, vol. 9(13), pages 1-11, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1507-:d:583706
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    References listed on IDEAS

    as
    1. Anderson, Douglas R. & Onitsuka, Masakazu, 2019. "Hyers–Ulam stability for a discrete time scale with two step sizes," Applied Mathematics and Computation, Elsevier, vol. 344, pages 128-140.
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