  Cosmological features of Barrow Holographic Dark Energy (BHDE), a recent
generalization of original Holographic dark energy with a richer structure, are
studied in the context of DGP brane, RS II brane-world, and the cyclic
universe. It is found that a flat FRW scenario with pressure less dust and a
dark energy component described as BHDE can accommodate late time acceleration
with Hubble horizon considered as infrared cut off even in the absence of
interaction between the dark sectors. Statefinder diagnostic reveals that these
model resemble $\Lambda CDM$ cosmology in future. It is found that BHDE
parameter $\Delta$, despite its theoretically constrained range of values, is
significant in describing the evolution of the universe, however, a classically
stable cosmological model cannot be obtained in the RS-II and DGP brane.
Viability of the models is also probed with observed Hubble data.
