Barrow entropic dark energy: A member of generalized holographic dark energy family

The holographic cut-off, in the formalism of generalized dark energy (HDE), is to depend on $L_\mathrm{IR} = L_\mathrm{IR} \left( L_\mathrm{p}, \dot \ddot \cdots, L_\mathrm{f}, a\right)$, where $L_\mathrm{p}$ and $L_\mathrm{f}$ are particle horizon future respectively, $a$ scale factor universe. Based such formalism, we showed that Barrow entropic (DE) model equivalent HDE respective cut-off determined by two ways -- (1) terms its derivative (2) derivative. Interestingly, turns out up-to first order or respectively. Such equivalence between extended scenario exponent entropy allows vary with cosmological expansion In both cases (whether a constant varies evolution), determine effective equation state (EoS) parameter from point view, which, comparing DE EoS parameter, further ensures HDE.