Modulo periodic Poisson stable solutions of dynamic equations on a time scale

TL;DR

This paper investigates the existence, uniqueness, and stability of modulo periodic Poisson stable solutions in dynamic equations on periodic time scales, introducing new definitions and employing reduction techniques to impulsive differential equations.

Contribution

It introduces novel definitions for Poisson stable functions on time scales and applies reduction techniques to establish key properties of solutions.

Findings

Proved existence and uniqueness of solutions

Established asymptotic stability under certain conditions

Provided an example confirming theoretical results

Abstract

The existence, uniqueness, and asymptotic stability of modulo periodic Poisson stable solutions of dynamic equations on a periodic time scale are investigated. The model under investigation involves a term which is constructed via a Poisson stable sequence. Novel definitions for Poisson stable as well as modulo periodic Poisson stable functions on time scales are provided, and the reduction technique to systems of impulsive differential equations is utilized to achieve the main result. An example which confirms the theoretical results is provided.