  In this work we study a non-flat Friedmann-Robertson-Walker universe filled
with a pressure-less dark matter (DM) and Barrow holographic dark energy (BHDE)
whose IR cutoff is the apparent horizon. Among various DE models, (BHDE) model
shows the dynamical enthusiasm to discuss the universe's transition phase.
According to the new research, the universe transitioned smoothly from a
decelerated to an accelerated period of expansion in the recent past. We
exhibit that the development of $q$ relies upon the type of spatial curvature.
Here we study the equation of state (EoS) parameter for the BHDE model to
determine the cosmological evolution for the non-flat universe. The (EoS)
parameter and the deceleration parameter (DP) shows a satisfactory behaviour,
it does not cross the the phantom line. We also plot the statefinder diagram to
characterize the properties of the BHDE model by taking distinct values of
barrow exponent $\triangle$. Moreover, we likewise noticed the BHDE model in
the $(\omega_{D}-\omega_{D}^{'})$ plane, which can furnish us with a valuable,
powerful finding to the mathematical determination of the statefinder. In the
statefinder trajectory, this model was found to be able to reach the $\Lambda
CDM$ fixed point.
