  Current observational data indicate that dark energy (DE) is a cosmological
constant without considering its conclusiveness evidence. Considering the
dynamic nature of $\Lambda$ individually as a function of time and the scale
factor, we review their effects on the gravitational waves. This article is a
continuation of the previous work \textit{JHEAp 36 (2022) 48-54}, in which DE
only was based on Hubble's parameter and/or its derivatives. For the DE model
based on the scale factor ($a^{-m}$), the results showed that the parameter $m$
is more limited as $ 2 < m \leqslant 3$ compared with the other models and due
to the small value of DE density at the early universe. It is only in the mode
$m=3$ that DE affects the low-frequency gravitational waves when its frequency
is less than the $10^{-3}$Hz in a matter-dominated epoch. The broad bound on
reducing the amplitude and the "B-B" polarization multipole coefficients, from
maximum to minimum, is for the models developed based on the Hubble parameter
function. There are primary sources of low- and very low-frequency GWs, such as
the coalescence of massive black hole binaries with $M_{bh} > 10^{3} M_{sun}$,
to determine the type of DE by mHz frequency space experiments (e.g., LISA) and
by nHz-range NANOGrav 15-year data.
