# On double q-Laplace transform and applications

## TL;DR

This paper introduces four q-analogs of the double Laplace transform, explores their properties, and demonstrates their application in solving q-functional and partial q-differential equations.

## Contribution

The paper presents new q-analogs of the double Laplace transform and establishes their properties and applications in solving specific q-equations.

## Key findings

- Four q-analogs of the double Laplace transform are defined.
- Main properties of these q-transforms are proved.
- Applications include solving q-functional and partial q-differential equations.

## Abstract

We introduce four q-analogs of the double Laplace transform and prove some of their main properties. Next we show how they can be used to solve some q-functional equations and partial q-differential equations.