Hyers–Ulam Stability for Cayley Quantum Equations and Its Application to h-Difference Equations

Abstract

The main purpose of this study is to clarify the Hyers–Ulam stability (HUS) for the Cayley quantum equation. In addition, the result obtained for all parameters is applied to HUS of h-difference equations with a specific variable coefficient using a new transformation.

On the solution of the Cayley impulsive dynamic control systems

“…In special, Pythagorean trigonometric identities hold exactly on any time scale. Dynamic equations satisfied by Cayley-type functions have a natural resemblance to the corresponding differential equations, Cayley h-difference equations [30], and Cayley quantum equations [31].…”

Ulam stability for nonautonomous quantum equations

“…In a series of recent papers [7][8][9] the authors introduced the study of Ulam stability for linear quantum (q-difference) equations of first order with a complex constant coefficient. See [1,2,19] for the literature on related topics.…”