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This paper is devoted to analyzing the critical phenomenon and phasetransition of quintessential Kerr-Newman-anti-de Sitter black hole in theframework of Maxwell equal-area law. For this purpose, we first derivethermodynamic quantities such as Hawking temperature, entropy and angularmomentum in the context of extended phase space. These quantities satisfySmarr-Gibbs-Dehum relation in the presence of quintessence matter. We thendiscuss the critical behavior of thermodynamic quantities through twoapproaches, i.e., van der Waals-like equation of state and Maxwell equal-arealaw. It is found that the latter approach is more effective to analyze thecritical behavior of the complicated black holes. Using equal-area law, we alsostudy phase diagram in $T-S$ plane and find an isobar which shows thecoexistence region of two phases. We conclude that below the criticaltemperature, black holes show a similar phase transition as that of van derWaals fluid. Finally, we study the effects of thermal fluctuations on thestability of this black hole.

Phase Transition and Thermal Fluctuations of Quintessential Kerr-Newman-AdS Black Hole