On Saigo Fractional $q$-Calculus of a General Class of $q$-Polynomials

Abstract

In this paper, we derive Saigo fractional $q$-integrals of the general class of $q$-polynomials and demonstrate their application by investigating $q$-Konhouser biorthogonal polynomial, $q$-Jacobi polynomials and basic analogue of the Kamp$\acute{e}$ de F$\acute{e}$riet function. We have also derived polynomials as a specific example of our significant findings.

Keywords

• saigo fractional $q$-integral operators
• general class of $q$-polynomials
• $q$-jacobi polynomials
• $q$-konhouser polynomials
• $q$-kampe de feriet function