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.
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