2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110023This paper aims to study the $q$-wavelet and the $q$-wavelet transforms, associated with the $q$-Bessel operator for a fixed $q\in ]0, 1[$. As an application, an inversion formulas of the $q$-Riemann-Liouville and $q$-Weyl transforms using $q$-wavelets are given. For this purpose, we shall attempt to extend the classical theory by giving their $q$-analogues.24 pagesQuantum AlgebraMathematical Physics33C15text