  Graph signal processing (GSP) is an effective tool in dealing with data
residing in irregular domains. In GSP, the optimal graph filter is one of the
essential techniques, owing to its ability to recover the original signal from
the distorted and noisy version. However, most current research focuses on
static graph signals and ordinary space/time or frequency domains. The
time-varying graph signals have a strong ability to capture the features of
real-world data, and fractional domains can provide a more suitable space to
separate the signal and noise. In this paper, the optimal time-vertex graph
filter and its Wiener-Hopf equation are developed, using the product graph
framework. Furthermore, the optimal time-vertex graph filter in fractional
domains is also developed, using the graph fractional Laplacian operator and
graph fractional Fourier transform. Numerical simulations on real-world
datasets will demonstrate the superiority of the optimal time-vertex graph
filter in fractional domains over the optimal time-vertex graph filter in
ordinary domains and the optimal static graph filter in fractional domains.
