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
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Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 3, 2020
Idioma: inglés
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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.