Generalized q-difference equation for the generalized q-operator r?s(Dq) and its applications in q-integrals

Abstract

In 2014, Fang [12] discovered a general q-exponential operator identity by solving a q-difference equation. Fang [12] developed some generalizations of q-integrals using this q-difference equation. Reshem and Saad [20] presented the solution to a generalized q-difference equation in q-operator form, which is a generalization of Fang’s work [12]. Using the q-difference equation technique, Reshem and Saad [20] discussed some properties of q-polynomials. In this paper, the generalized q-difference equation technique is used to generalize some well-known integrals such as fractional q-integrals, the q-Barnes contour integral, and Ramanujan q-integrals.