Charged AdS black holes in Gauss-Bonnet gravity and nonlinear electrodynamics

New five-dimensional charged AdS black hole solutions are found in Einstein-Gauss-Bonnet gravity and the nonlinear electrodynamics. These solutions include regular black holes as well as extremal black holes. The first law of the black hole thermodynamics is confirmed in the extended phase space where the cosmological constant is treated as the pressure. The first and second order phase transitions are investigated by observing the behavior of the heat capacity at constant pressure and the Gibbs free energy. In addition, the equation of state for the black holes and their P-V criticality are studied. Finally, the critical exponents are found to be the same as those of the Van der Waals fluid.