The current study takes into account the evolution of a fractal universe with holographic dark energy through Barrow entropy and dark matter, i.e. without pressure, which interact with one another through mutual interaction. The interaction term for this model is then rebuilt by using the Hubble length as the IR cut-off scale. We represent Barrow holographic dark energy as Nojiri–Odintsov generalized holographic dark energy in fractal universe. The cosmological parameters that change over the course of cosmic history are looked at from the early matter-dominated period through the late time acceleration. The results of the study indicate that the cosmos recently underwent a smooth transition from a decelerated to an accelerated phase of expansion. We also found that the Barrow holographic dark energy equation of state parameter exhibits a rich behavior, lying in the quintessence regime, the phantom regime, or experiencing the phantom-divide crossing during evolution, depending on the values of the coupling term $b^2$ and the Barrow exponent $\mathrm{\Delta }$. It has been reported on the evolution of the model’s Hubble parameter and a comparison with the most recent cosmic chronometer data. The stability of the model has also been examined in order to determine its viability, with the square of sound speed being taken into account.

目前的研究考虑了通过巴罗熵和暗物质（即没有压力）通过相互作用而相互作用的具有全息暗能量的分形宇宙的演化。然后使用哈勃长度作为 IR 截止尺度重建该模型的相互作用项。我们将 Barrow 全息暗能量表示为分形宇宙中的 Nojiri-Odintsov 广义全息暗能量。从早期的物质主导时期到晚期的时间加速，研究了在宇宙历史过程中发生变化的宇宙学参数。研究结果表明，宇宙最近经历了从减速膨胀阶段到加速膨胀阶段的平稳过渡。$b^{\mathrm{2个}}$和巴罗指数$\mathrm{△}$. 已经报道了模型的哈勃参数的演变以及与最新的宇宙天文台数据的比较。还检查了模型的稳定性以确定其可行性，其中考虑了声速的平方。