  In this paper, we have studied continuous fractional wavelet transform
(CFrWT) in $n$-dimensional Euclidean space $\mathbb{R}^n$ with dilation
parameter $\boldsymbol a=(a_{1},a_{2},\ldots,a_{n}),$ such that none of
$a_{i}'s$ are zero. Necessary and sufficient condition for the admissibility of
a function is established with the help of fractional convolution. Inner
product relation, reconstruction formula and the reproducing kernel for the
CFrWT depending on two wavelets are obtained. Heisenberg's uncertainty
inequality and Local uncertainty inequality for the CFrWT are obtained.
Finally, boundedness of the transform on the Morrey space
$L^{1,\nu}_{M}(\mathbb{R}^n)$ and the estimate of
$L^{1,\nu}_{M}(\mathbb{R}^n)$-distance of the CFrWT of two argument functions
with respect to different wavelets are discussed.
