Stability analysis of first-order impulsive nonautonomous system on timescales |
| |
| Authors: | Akbar Zada Bakhtawar Pervaiz Syed Omar Shah Jiafa Xu |
| |
| Affiliation: | 1. Department of Mathematics, University of Peshawar, Peshawar, 25000 Pakistan;2. Department of Physical and Numerical Sciences, Qurtuba University of Science and Information Technology Peshawar, Dera Ismail Khan, Pakistan;3. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331 China |
| |
| Abstract: | In this manuscript, we present the existence, uniqueness, β-Ulam-Hyers stability, and β-Ulam-Hyers-Rassias stability of semilinear nonautonomous impulsive dynamic systems on timescales, with the help of fixed point approach. We use Grönwall inequality on timescale, abstract Gröwall lemma, and Picard operator as basic tools to develop our main results. At the end, an example is given to demonstrate the validity of our main theoretical result. |
| |
| Keywords: | Banach fixed point theorem dynamic system impulses timescale semilinear nonautonomous system β-Ulam-Hyers stability |
|
|
