On (<i>p</i>,<i>q</i>)-Sumudu and (<i>p</i>,<i>q</i>)-Laplace Transforms of the Basic Analogue of Aleph-Function

Abstract

In this paper, we introduce the definitions of Sumudu and Laplace transforms of first and second kind in quantum calculus by using functions of several variables. On account of the general nature of the ( p , q ) -analogue of Aleph-function, a large number of new and known results for these transforms were obtained. Also, we obtain some interesting relationships and identities for these transforms. We also derive some correlations among Aleph function and the above-mentioned integral transforms in quantum calculus.

Keywords

• integral transforms
• basic hypergeometric functions
• q-calculus