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 Rajkovi ´ c–Marinkovi ´ c–Stankovi ´ c 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.