The fractional wavelet transform is an extension of the conventional wavelet transform in the context of the fractional Fourier transform. In current work, we present the natural link between the fractional Fourier transform and conventional wavelet transform. We apply this relation to provide the different proof of some fundamental properties of the fractional wavelet transform such as the orthogonality relation, inversion formula and reproducing kernel. Based on these properties and relation, we formulate Pitt�s inequality associated with the fractional Fourier transform. © 2021, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.