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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.

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