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

Abstract

Abstract 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.

Keywords

• Homogeneous q-difference equations
• Verma–Jain polynomials
• Srivastava–Agarwal type generating functions
• Fractional q-integrals
• U ( n + 1 ) $U(n+1)$ type generating function