<i>β</i>–Hyers–Ulam–Rassias Stability of Semilinear Nonautonomous Impulsive System
oleh: Xiaoming Wang, Muhammad Arif, Akbar Zada
| Format: | Article |
|---|---|
| Diterbitkan: | MDPI AG 2019-02-01 |
Deskripsi
In this paper, we study a system governed by impulsive semilinear nonautonomous differential equations. We present the <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>⁻Ulam stability, <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>⁻Hyers⁻Ulam stability and <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>⁻Hyers⁻Ulam⁻Rassias stability for the said system on a compact interval and then extended it to an unbounded interval. We use Grönwall type inequality and evolution family as a basic tool for our results. We present an example to demonstrate the application of the main result.