Generalizations of fractional q-integrals involving Cauchy polynomials and some applications

Abstract

In this paper, we demonstrate the technique of iterations and generalize Riemann-Liouville fractional q-integrals involving Cauchy polynomials. We obtain the generalizations of Srivastava-Agarwal type generating functions by generalized fractional q-integrals involving Cauchy polynomials. Moreover, we also derive generating functions for Rajković-Marinković-Stanković polynomials involving Cauchy polynomial by fractional q-integrals. At last, we deduce a generalization of Jackson's transformation formula by fractional q-integrals involving Cauchy polynomials.