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Abstract
Fractional calculus and q-calculus have emerged as significant areas of mathematical analysis due to their wide applications in special functions, mathematical physics, and related fields. In this paper, we investigate certain q-Weyl fractional integral operators associated with generalized basic hypergeometric functions. A q-analogue of the Weyl fractional integral operator is employed to derive new integral representations and operational formulas for generalized multibasic hypergeometric series. The obtained results provide extensions of several classical and q-analogue identities within the framework of fractional q-calculus. Furthermore, the action of the proposed q-Weyl fractional integral operator on various important classes of q-polynomials, including q-Laguerre, Wall, Stieltjes–Wigert, q-Konhauser, and other related q-polynomials, is established. Several special cases are derived as consequences of the main results, demonstrating the applicability and generality of the developed formulas. The present work establishes a connection between fractional integral operators, generalized basic hypergeometric functions, and q-polynomial theory, contributing to the advancement of q-analysis and special function theory. These results may be useful for further investigations in fractional q-calculus, orthogonal polynomials, and applications in mathematical physics and related disciplines.
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