  We investigate how three different possibilities of neutrino mass
hierarchies, namely normal, inverted, and degenerate, can affect the
observational constraints on three well known dynamical dark energy models,
namely the Chevallier-Polarski-Linder, logarithmic, and the
Jassal-Bagla-Padmanabhan parametrizations. In order to impose the observational
constraints on the models, we performed a robust analysis using Planck 2015
temperature and polarization data, Supernovae type Ia from Joint Light curve
analysis, baryon acoustic oscillations distance measurements, redshift space
distortion characterized by $f(z)\sigma_8(z)$ data, weak gravitational lensing
data from Canada-France-Hawaii Telescope Lensing Survey, and cosmic
chronometers data plus the local value of the Hubble parameter. We find that
different neutrino mass hierarchies return similar fit on almost all model
parameters and mildly change the dynamical dark energy properties.
