Opuscula Math. 35, no. 6 (2015), 867-887
http://dx.doi.org/10.7494/OpMath.2015.35.6.867

Opuscula Mathematica

# Inversion of the Riemann-Liouville operator and its dual using wavelets

C. Baccar
H. Herch
F. Meherzi

Abstract. We define and study the generalized continuous wavelet transform associated with the Riemann-Liouville operator that we use to express the new inversion formulas of the Riemann-Liouville operator and its dual.

Keywords: inverse problem, Riemann-Liouville operator, Fourier transform, wavelets.

Mathematics Subject Classification: 35R30, 42B10, 42C40.

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• C. Baccar
• Higher Institute of Informatics of El Manar 2, Department of Applied Mathematics, Rue Abou Raïhan El Bayrouni - 2080 Ariana, Tunisia
• Department of Mathematics, Preparatory Institute for Engineering Studies El Manar, 2092 El Manar 2 Tunis, Tunisia
• H. Herch
• F. Meherzi
• Communicated by Semyon B. Yakubovich.
• Revised: 2014-12-29.
• Accepted: 2015-01-05.
• Published online: 2015-06-06.