# Almost periodic functions on the quantum time scale and applications

## TL;DR

This paper introduces new concepts of almost periodic functions on the quantum time scale, explores their properties, and applies these to establish the existence of solutions in quantum neural networks.

## Contribution

It proposes two types of almost periodic functions on the quantum time scale and applies them to neural network models, extending classical concepts to quantum calculus.

## Key findings

- Established existence and uniqueness of almost periodic solutions for dynamic equations on the quantum time scale.
- Provided an equivalent definition of almost periodic functions in this context.
- Applied the theory to high-order Hopfield neural networks on the quantum time scale.

## Abstract

In this paper, we first propose two types of concepts of almost periodic functions on the quantum time scale. Secondly, we study some basic properties of almost periodic functions on the quantum time scale. Thirdly, based on these, we study the existence and uniqueness of almost periodic solutions of dynamic equations on the quantum time scale by Lyapunov method. Then, we give a equivalent definition of almost periodic functions on the quantum time scale. Finally, as an application, we propose a class of high-order Hopfield neural networks on the quantum time scale and establish the existence of almost periodic solutions of this class of neural networks.