  Employing the fractional derivatives, we construct a more elaborate
classification of phase transitions compared to the original Ehrenfest
classification. In this way, a thermodynamic system can even undergo a
fractional-order phase transition. We use this method to restudy the charged
AdS black hole and Van der Waals fluids and find that at the critical point
they both have a $4/3$-order phase transition, but not the previously
recognized second-order one.
