Existence, uniqueness and stability of semilinear nonautonomous impulsive systems on time scales

Abstract

This primer article focuses on the existence, uniqueness and Ulams stability of semilinear nonautonomous dynamic problem with impulses on time scales, by utilizing fixed point method. We establish our results with the help of abstract Grönwall inequality and Picard operator. We utilize some assertions to overcome difficulties. To demonstrate our main result, we provide an example at the end.

Keywords:

• Semilinear nonautonomous system
• time scale
• impulses
• Banach fixed point principle
• dynamic system
• Ulam–Hyers stability

2010 Mathematics Subject Classifications:

• 34N05
• 34G20
• 35B35
• 45J05

Disclosure statement

No potential conflict of interest was reported by the author(s).