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**[S. K. Q. Al-Omari]{}**

Department of Applied Sciences; Faculty of Engineering Technology; Al-Balqa’

Applied University; Amman 11134; Jordan

s.k.q.alomari@fet.edu.jo

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**Abstract**

Some $q$-analogues of classical integral transforms have recently been investigated by many authors in diverse citations. The $q$-analogues of the Natural transform are not known nor used. In the present paper, we are concerned with definitions and investigations of the $q$-theory of the Natural transform and some applications. We present two types of $q$-analogues of the cited transform on given sets and get results of the nominated analogues for certain class of functions of special type. We declare here that given results are new and they complement recent known results related to $q$-Laplace and $q$-Sumudu transforms. Over and above, we present some supporting examples to illustrate effectiveness of the given results .

**Keywords :** $q$-Sumudu transform; $q$-Laplace transform; $q $-Natural transform; $q$-Bessel function.

Introduction
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The study of $q$-analogues of classical integral transforms has not yet been developed to a great extent. This partially can be explained by the fact that one is not very familiar with the $q$-theory and that basic $q$-integral transforms do not occur frequently in physics. It by no means our aim to 