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On the Bielecki–Ulam’s Type Stability Results of First Order Non-linear Impulsive Delay Dynamic Systems on Time Scales

  • Shah, Syed Omar [1] ; Zada, Akbar [2] ; Muzamil, Muzamil [1] ; Rizwan, Rizwan [3]
    1. [1] Qurtuba University of Science and Information Technology

      Qurtuba University of Science and Information Technology

      Pakistán

    2. [2] University of Peshawar

      University of Peshawar

      Pakistán

    3. [3] University of Buner
    Mostrar afiliaciones +
  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 3, 2020
  • Idioma: inglés
  • DOI: 10.1007/s12346-020-00436-8
  • Enlaces
  • Resumen

    • In this manuscript, we present the existence and uniqueness of solution of first order non-linear impulsive delay dynamic systems on time scales, with the help of fixed point approach. Further, we investigate the Bielecki–Ulam–Hyers stability and Bielecki–Ulam–Hyers–Rassias stability of the proposed model. We use Grönwall’s inequality on time scales, Banach contraction principle, Picard operator and Lipschitz condition as a basic tools to develop our main results. Also, two examples are provided to illustrate the obtained results.

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