Geodesic
Inversion Formulas for the q-Riemann-Liouville and q-Weyl Transforms Using Wavelets
Fractional calculus and applied analysis, Tome 10 (2007) no. 4, pp. 327-342.

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This paper aims to study the q-wavelets and the continuous q-wavelet transforms, associated with the q-Bessel operator for a fixed q ∈]0, 1[. Using the q-Riemann-Liouville and the q-Weyl transforms, we give some relations between the continuous q-wavelet transform, studied in [3], and the continuous q-wavelet transform associated with the q-Bessel operator, and we deduce formulas which give the inverse operators of the q-Riemann-Liouville and the q-Weyl transforms.
Keywords: q-Bessel Operator, q-Wavelet, q-Riemann-Liou-Ville, q-Weyl Operators, 42A38, 42C40, 33D15, 33D60 
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     title = {Inversion {Formulas} for the {q-Riemann-Liouville} and {q-Weyl} {Transforms} {Using} {Wavelets}},
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Fitouhi, Ahmed; Bettaibi, Néji; Binous, Wafa. Inversion Formulas for the q-Riemann-Liouville and q-Weyl Transforms Using Wavelets. Fractional calculus and applied analysis, Tome 10 (2007) no. 4, pp. 327-342. http://geodesic.mathdoc.fr/item/FCAA_2007_10_4_a0/