  In present research, we construct Kaniadakis holographic dark energy (KHDE)
model within a non-flat Universe by considering the Friedmann-Robertson-Walker
(FRW) metric with open and closed spatial geometries. We therefore investigate
cosmic evolution by employing the density parameter of the dark energy (DE),
the equation of state (EoS) parameter and the deceleration parameter (DP). The
transition from decelerated to accelerated expanding phase for the KHDE
Universe is explained through dynamical behavior of DP. With the classification
of matter and DE dominated epochs, we find that the Universe thermal history
can be defined through the KHDE scenario, and moreover, a phantom regime is
experienceable. The model parameters are constrained by applying the newest
$30$ data cases of $H(z)$ measurements, over the redshift span $0.07 \leq z
\leq 2.36$, and the distance modulus measurement of the recent Union $2.1$ data
set of type Ia supernovae. The classical stability of KHDE model has also been
addressed.
