Abstract

The ${\bf N}$-transform (so-called natural transform) of a function, which may combine Laplace and Sumudu transforms, has been introduced and investigated. Recently $q$-analogues of the ${\bf N}$-transform has been presented and studied. Among $q$-extensions of a number of polynomials and functions, the $q$-Humbert functions and some of their interesting identities and properties have recently been introduced and provided. In this paper, we aim to present $q$-natural transforms of a finite product of the $q$-Humbert functions. Some particular cases of our main identities are also considered.

Keywords and Phrases

Laplace transform, Sumudu transform, Natural transform, $q$-Laplace transforms, $q$-Sumudu transforms, $q$-Natural transforms, $q$-Gamma functions, $q$-Humbert functions.

A.M.S. subject classification

33D45, 33D60, 33D05, 33D15, 05A30.

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