  In this paper, we have extended and deepened the study on fractional order
phase transition (FPT) of a charged AdS black hole performed in [1]. We have
carried out a detailed analysis of FPT for several AdS black hole prototypes:
black hole surrounded by quintessence background, 5D Gauss-Bonnet, D
dimensional RN-AdS BH, and lastly Kerr black holes. We have shown that the 4/3
order FPT at critical points obtained in [1] still holds for the first three
black holes systems, while for Kerr black holes, the fractional order is rather
1/3. These results suggest two remarkable features: Firstly 4/3 order phase
transition can be assumed for asymptotically AdS black holes spherical
solutions, secondly the fractional order is not universal and can be affected
by the geometric symmetry.
