# New approach to generalized Mittag-Leffler function via quantum calculus

## TL;DR

This paper introduces a novel q-analogue extension of the Mittag-Leffler function, exploring its properties like integral representation, q-differentiation, and q-Laplace transform, with applications demonstrated through particular cases.

## Contribution

It presents the first q-analogue extension of the Mittag-Leffler function along with its fundamental properties and potential applications.

## Key findings

- Derived integral representation of the q-Mittag-Leffler function
- Established q-differentiation and q-Laplace transform formulas
- Provided specific cases demonstrating applications of the new function

## Abstract

We aim to introduce a new extension of Mittag-Leffler function via q-analogue and obtained their significant properties including integral representation, q-differentiation, q-Laplace transform, image formula under q-derivative operators. We also consider some particular cases to give the applications of our main results.