Stability Analysis of the First Order Non-linear Impulsive Time Varying Delay Dynamic System on Time Scales

In this paper, we study Hyers–Ulam stability and Hyers–Ulam–Rassias stability of first order non-linear impulsive time varying delay dynamic system on time scales, via a fixed point approach. We obtain some results of existence and uniqueness of solutions by using Picard operator. The main tools for...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2019-12, Vol.18 (3), p.825-840
Main Authors: Shah, Syed Omar, Zada, Akbar, Hamza, Alaa E.
Format: Article
Language:English
Subjects:
Delay
Difference and Functional Equations
Dynamic stability
Dynamical systems
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
Stability analysis
Time
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Summary:In this paper, we study Hyers–Ulam stability and Hyers–Ulam–Rassias stability of first order non-linear impulsive time varying delay dynamic system on time scales, via a fixed point approach. We obtain some results of existence and uniqueness of solutions by using Picard operator. The main tools for our results are the Grönwall’s inequality on time scales, abstract Grönwall lemma and Banach contraction principle. In order to overcome difficulties arises in our considered model, we pose some conditions along with Lipchitz condition. At the end, an example is given that shows the validity of our main results.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-019-00315-x