  Pulsar timing arrays (PTAs) have the potential to detect Nanohertz
gravitational waves (GWs) that are usually generated by the individual
inspiraling supermassive black hole binaries (SMBHBs) in the galactic centers.
The GW signals as cosmological standard sirens can provide the absolute cosmic
distances, thereby can be used to constrain the cosmological parameters. In
this paper, we analyze the ability of future SKA-era PTAs to detect the
existing SMBHBs candidates assuming the root mean square of timing noise
$\sigma_t=20\ {\rm ns}$, and use the simulated PTA data to constrain the
interacting dark energy (IDE) models with energy transfer rate $Q = \beta
H\rho_c$. We find that, the future SKA-era PTAs will play an important role in
constraining the IDE cosmology. Using only the mock PTA data consisting of 100
pulsars, we obtain $\sigma(H_0)=0.239\ {\rm km} \ {\rm s}^{-1} {\rm Mpc}^{-1}$
and $\sigma(\Omega_m)=0.0103$ in the I$\Lambda$CDM model, which are much better
than the results from the Planck TT, TE, EE+lowE. However, the PTA data cannot
provide a tight constraint on the coupling parameter $\beta$ compared with
Planck, but the data combination of Planck+PTA can provide a rather tight
constraint, i.e., $\sigma(\beta)=0.00232$, since the PTA data could break the
parameter degeneracies inherent in CMB. In the I$w$CDM model, we obtain
$\sigma(\beta)=0.00137$ and $\sigma(w)=0.0492$ from the Planck+PTA data
combination. In addition, we find that with the increase of the number of
pulsars in PTA, the constraint results from the Planck+PTA will be further
improved to some extent. We show that the observations of Nanohertz GWs with
future SKA-era PTAs will provide a powerful tool for exploring the nature of
dark energy and measuring the coupling between dark energy and dark matter.
