Thermodynamics of Barrow Einstein-power-Yang-Mills AdS black hole in the restricted phase space

As we know that due to the quantum gravitational effects black hole horizons are ``fractalized'' into a sphereflake by Barrow. Based on this issue, in this work we investigate the phase structure and stability of the Einstein-Power-Yang-Mills AdS black holes with the fractal structure on the black hole horizon in the restricted phase space. Through the thermodynamics first law and the Smarr relation in the restricted phase space, we observe that the mass parameter is understood as the inter energy and the Smarr relation is not a homogeneous function of order one for all quantities due to the fractal structure. And the fractal structure can be regarded as a phase transition probe. When this system with the fixed central charge there exists a novel phenomena: the supercritical phase transition. Furthermore the effects of the fractal parameter and non-linear Yang-Mills parameter on the thermodynamics stability of this system are also investigated.