On Transformation Involving Basic Analogue of Multivariable H-Function

In this article, fractional order q-integrals and q-derivatives involving a basic analogue of multivariable H-function have been obtained. We give an application concerning the basic analogue of multivariable H-function and q-extension of the Leibniz rule for the fractional q-derivative for a product of two basic functions. We also give the corollary concerning basic analogue of multivariable Meijer’s G-function as a particular case of the main result.

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

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.

New Generating Function Relations for the q-Generalized Cesàro Polynomials

The main purpose of this paper is to examine a basic (or q-) analogue of the generalized Cesàro polynomials described here. We derive a bilateral q-generating function involving basic analogue of Fox’s H-function and q-generalized Cesàro polynomials.