Fractional order phase transition based on Q − Φ criticality of RN-AdS black hole

We consider the Q − Φ criticality of RN-AdS black hole in four-dimensional spacetime. Especially, by employing the fractional derivative we reanalyze the order of phase transition at the critical point. By means of this fine-grained classification of phase transition, it is found that at the critical point it is a 4/3-order, but not the second-order phase transition. This result is the same as that obtained in a previous work on the basis of P − V criticality.