Superconductivity is analysed based on the product-like fractal measure approach with fractal dimension $\alpha$ introduced by Li and Ostoja-Starzewski in their attempt to explore anisotropic fractal elastic media. Our study shows the emergence of a massless state at the boundary of the superconductor and the simultaneous occurrence of isothermal and adiabatic processes in the superconductor depending on the position of the electrons. Several physical quantities were found to be position-dependent comparable with those arising in heavy doping and p–n junction. At the boundary of the superconductor, a shrinkage of the magnetic field was observed, leading to a scenario equivalent to the Meissner–Ochsenfeld effect. An enhancement of the London penetration depth is revealed and such an improvement was observed in pnictides at the onset of commensurate spin-density-wave order inside the superconducting phase at zero temperature. The Bardeen–Cooper–Schrieffer theory was also analysed and the appearance of zero-energy states is detected. Nucleation of superconductivity in a bulk was also studied. The system acts as a quantum damped harmonic oscillator and our analysis showed that type-I superconductivity occurs when $\kappa <\sqrt{2}/(1+\alpha )$, whereas type II occurs for $\kappa >\sqrt{2}/(1+\alpha )$, where $\kappa$ is the Ginzburg–Landau parameter. The transition at the passage from the ‘genuine’ to the ‘intermediate’ type-I estimates $0.767767<\alpha \le 1$.

基于具有分形维数的类似产品的分形测量方法来分析超导性 $\alpha$由Li和Ostoja-Starzewski提出，旨在探索各向异性的分形弹性介质。我们的研究表明，在超导体的边界处出现了无质量状态，并且在超导体中同时发生了等温和绝热过程，这取决于电子的位置。发现一些物理量与重掺杂和p–n产生的物理量具有位置相关性交界处。在超导体的边界处，观察到磁场的收缩，从而导致了相当于迈斯纳-奥克森费尔德效应的情形。揭示了伦敦渗透深度的增加，并且在零温度下在超导相内部相应的自旋密度波阶开始时，在光敏剂中观察到了这种改善。还分析了Bardeen-Cooper-Schrieffer理论，并检测了零能态的出现。还研究了本体中的超导形核。该系统起着量子阻尼谐波振荡器的作用，我们的分析表明，当$\kappa <\sqrt{\mathrm{2个}}/（\mathrm{1个}+\alpha ）$，而II型发生在 $\kappa >\sqrt{\mathrm{2个}}/（\mathrm{1个}+\alpha ）$， 在哪里 $\kappa$是Ginzburg–Landau参数。从“正版”到“中级” I型估计的过渡$0.767767<\alpha \le \mathrm{1个}$。