# On two $(p,q)$-analogues of the Laplace transform

## TL;DR

This paper introduces two new $(p,q)$-Laplace transforms, explores their properties, and demonstrates their use in solving $(p,q)$-linear difference equations, expanding the mathematical toolkit for $(p,q)$-calculus.

## Contribution

The paper presents novel $(p,q)$-Laplace transforms and establishes their properties, providing new methods for solving related difference equations.

## Key findings

- Two $(p,q)$-Laplace transforms are defined and analyzed.
- Properties of the $(p,q)$-Laplace transforms are proved.
- Applications include solving $(p,q)$-linear difference equations.

## Abstract

Two $(p,q)$-Laplace transforms are introduced and their relative properties are stated and proved. Applications are made to solve some $(p,q)$-linear difference equations.