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In this study, we delve into the analysis of phase transitions by employingapproximated formulas for the horizon radius. The novelty of this work isapparent in the first-time determination of analytical expressions for criticalpoints for charged and Kerr-Newman Anti-de Sitter (AdS) black holes withinRastall gravity, considering the presence of perfect fluid matter. This pavesthe way for exploring the distinctiveness of fractional order phase transitionsin these AdS black holes. Additionally, the analysis involves calculatingcritical exponents, offering insights into the behavior of crucialthermodynamic quantities near the inflection point. The examination of howperfect fluid matter influences phase transitions reveals various criticalbehaviors, demonstrating that the variation in phase transition is contingenton the intensity of perfect fluid matter. Notably, this variation is portrayedby a linearly increasing trajectory with the escalation of this intensity.

Thermodynamic Features of Ads Black Holes within Rastall Gravity and Perfect Fluid Matter Framework