  We study the cosmological evolution of a nonflat Friedmann-Robertson-Walker
Universe filled by pressureless dark matter and Barrow Holographic Dark Energy
(BHDE). The latter is a dark energy model based on the holographic principle
with Barrow entropy instead of the standard Bekenstein-Hawking one. By assuming
the apparent horizon of the Universe as IR cutoff, we explore both the cases
where a mutual interaction between the dark components of the cosmos is
absent/present. We analyze the behavior of various model parameters, such as
the BHDE density parameter, the equation of state parameter, the deceleration
parameter, the jerk parameter and the square of sound speed. We also comment on
the observational consistency of our predictions, showing that the interacting
model turns out to be favored by recent experimental constraints from
Planck+WP+BAO, SNIa+CMB+LSS and Union2 SNIa joint analysis over the
non-interacting one. The thermal stability of our framework is finally
discussed by demanding the positivity of the heat capacities and
compressibilities of the cosmic fluid.
