Generalized homogeneous q -difference equations for q -polynomials and their applications to generating functions and fractional q -integrals

摘要

In this paper, our aim is to build generalized homogeneous q-difference equations for q-polynomials. We also consider their applications to generating functions and fractional q-integrals by using the perspective of q-difference equations. In addition, we also reveal relevant relations of various special cases of our main results involving some known results.