Saigo fractional q-integral involving the generalized q-hypergeometric series and a general class of q-polynomials

Abstract

The fractional q-calculus has attracted the interest of a large number of academics over the last four decades or so, due mainly to a wide range of applications that cover natural sciences to social sciences. Many fractional q-calculus operators, particularly those involving various q-special functions, have been deeply studied and widely applied. In this paper, we aim to establish certain image formulas of Saigo fractional q-integral operators involving the product of generalized q-hypergeometric series and a general class of q-polynomials that are primarily expressed in terms of generalized q-hypergeometric series in a systematic manner. We demonstrate their use by studying q-Konhouser biorthogonal polynomials and q-Jacobi polynomials. Additionally, some fascinating special cases of our main findings are taken into consideration, and pertinent connections between some of the findings presented here and those from earlier studies are also made.

Keywords:

• GCq-Ps
• q-hypergeometric series
• q-integrals
• q-Jacobi polynomials
• q-Konhouser biorthogonal
• Saigo’s fractional

2010Mathematics Subject Classification:

• 26A33
• 33D15
• 33D60
• 33D90

Disclosure statement

There is no conflict of interest regarding the publication of this article.

Data availability statement

No data were used to support this study.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.