  One of the key challenges in the area of signal processing on graphs is to
design transforms and dictionaries methods to identify and exploit structure in
signals on weighted graphs. In this paper, we first generalize graph Fourier
transform (GFT) to graph fractional Fourier transform (GFRFT), which is then
used to define a novel transform named spectral graph fractional wavelet
transform (SGFRWT), which is a generalized and extended version of spectral
graph wavelet transform (SGWT). A fast algorithm for SGFRWT is also derived and
implemented based on Fourier series approximation. The potential applications
of SGFRWT are also presented.
