Shapiro’s uncertainty principles and scalogram associated with the Riemann-Liouville wavelet transform

The Riemann-Liouville operator has been extensively investigated and has witnessed a remarkable development in numerous fields of harmonic analysis over a couple of decades. The aim of this article is to explore two more aspects of the time-frequency analysis associated with the Riemann-Liouville wavelet transform, including the Shapiro uncertainty principle and the scalogram.