  In graph signal processing, many studies assume that the underlying network
is undirected. Although the digraph model is rarely adopted, it is more
appropriate for many applications, especially for real world networks. In this
paper, we present a general framework for extending the graph signal processing
to directed graphs in graph fractional domain. For this purpose, we consider a
new definition for fractional Hermitian Laplacian matrix on directed graph and
generalize the spectral graph fractional Fourier transform to directed graph
(DGFRFT). Based on our new transform, we then define filtering, which is used
in reducing unnecessary noise superimposed on temperature data. Finally, the
performance of the proposed DGFRFT approach is also evaluated through numerical
experiments using real-world directed graphs.
