On Some q-Analogues of the Natural Transform and Further Investigations

TL;DR

This paper introduces and investigates new q-analogues of the Natural transform, expanding the q-transform theory with applications and examples, complementing existing q-Laplace and q-Sumudu transforms.

Contribution

It defines and explores the q-theory of the Natural transform, providing new analogues and demonstrating their effectiveness through examples.

Findings

New q-analogues of the Natural transform are proposed.

Results are obtained for specific classes of functions.

The work complements existing q-Laplace and q-Sumudu transforms.

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 .