In this study, the fractal neutrons diffusion equation is constructed based on the concept of fractal anisotropy and product-like fractal measure introduced by Li and Ostoja-Starzewski using the method of dimensional regularization. In this approach, the global forms of dynamical equations are cast in forms involving integer-order integrals while the local forms are expressed by partial differential equations with derivatives of integer order. This theory is characterized by an effective buckling which varies with distance and a diffusion damping characterized by a spatially variable coefficient. These terms are major in nuclear reactor physics since the magnitude of energy dissipation in fission depends on the position and nature of interaction. We have discussed the cases of parallelepiped and finite cylinder reactors. In both geometrical types of reactors, it was observed that the ratio of the maximum flux to the average flux is too small since the uniformization of the heat fabrication and the fuel burn-up in the nuclear reactor is potential. This has important consequences on safety of the fuel operation and on the types of nuclear materials used in nuclear engineering reactors. Further details are discussed as well.

本研究基于Li和Ostoja-Starzewski引入的分形各向异性和类积分形测度的概念，采用维数正则化的方法构建了分形中子扩散方程。在这种方法中，动力学方程的全局形式以涉及整数阶积分的形式进行转换，而局部形式则由具有整数阶导数的偏微分方程表示。该理论的特征在于随距离变化的有效屈曲和以空间可变系数为特征的扩散阻尼。这些术语在核反应堆物理学中很重要，因为裂变能量耗散的大小取决于相互作用的位置和性质。我们已经讨论了平行六面体和有限圆柱反应堆的情况。在两种几何类型的反应堆中，观察到最大通量与平均通量的比率太小，因为核反应堆中的热制造和燃料燃烧的均匀化是潜在的。这对燃料运行的安全和核工程反应堆中使用的核材料类型具有重要影响。还讨论了进一步的细节。