Inversion formulas for \(q\)-Riemann-Liouville and \(q\)-Weyl transforms (Q2381908)

This paper involves inversion formulas with \(q\)-integro-differential operators. A new proof of the inversion formula for the \(q\)-analogue of Riemann-Liouville and \(q\)-Weyl transform is given by introducing some \(q\)-analogues of fractional transforms. The \(q\)-integral of Weber and Schafheitlin [see \textit{T. H. Koornwinder} and \textit{R. F. Swarttouw}, Trans. Am. Math. Soc. 333, 445--461 (1992; Zbl 0759.33007)] are used to give a simple expression of the \(q\)-analogue of topological isomorphism.