Hyers-Ulam stability of second-order linear dynamic equations on time scales

TL;DR

This paper proves the Hyers-Ulam stability for second-order linear dynamic equations on time scales, showing that approximate solutions are close to exact solutions, unifying continuous and discrete cases.

Contribution

It extends the Hyers-Ulam stability concept to second-order linear dynamic equations on arbitrary time scales, providing a unified framework.

Findings

Established Hyers-Ulam stability for second-order equations on time scales

Demonstrated existence of exact solutions near approximate ones

Unified continuous and discrete dynamic equations stability analysis

Abstract

We establish the stability of second-order linear dynamic equations on time scales in the sense of Hyers and Ulam. To wit, if an approximate solution of the second-order linear equation exists, then there exists an exact solution to the dynamic equation that is close to the approximate one.