  We perform Markov chain Monte Carlo analyses to put constraints on the
non-flat $\phi$CDM inflation model using Planck 2015 cosmic microwave
background (CMB) anisotropy data and baryon acoustic oscillation distance
measurements. The $\phi$CDM model is a consistent dynamical dark energy model
in which the currently accelerating cosmological expansion is powered by a
scalar field $\phi$ slowly rolling down an inverse power-law potential energy
density. We also use a physically consistent power spectrum for energy density
inhomogeneities in this non-flat model. We find that, like the
closed-$\Lambda$CDM and closed-XCDM models, the closed-$\phi$CDM model provides
a better fit to the lower multipole region of the CMB temperature anisotropy
data compared to that provided by the tilted flat-$\Lambda$CDM model. Also,
like the other closed models, this model reduces the tension between the Planck
and the weak lensing $\sigma_8$ constraints. However, the higher multipole
region of the CMB temperature anisotropy data are better fit by the tilted
flat-$\Lambda$CDM model than by the closed models.
