  In this article, we have studied the convergence behavior of the
Dirichlet-Neumann waveform relaxation algorithms for time-fractional
sub-diffusion and diffusion wave equations in 1D \& 2D for regular domains,
where the dimensionless diffusion coefficient takes different constant values
in different subdomains. From numerical experiments, we first capture the
optimal relaxation parameters. Using these optimal relaxation parameters, our
analysis estimates the rate of change of the convergence behavior against the
fractional order and time. We have performed our analysis in multiple subdomain
cases for both in 1D \& 2D.
