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This article addresses critical challenges in the transition to clean energy sources by highlighting the importance of advanced mathematical modeling and computational techniques in turbine design and operation. Specifically, we extend and generalize the work of Camporeale to advance the modeling of hydrogen turbine systems. By utilizing conformable calculus, we develop dynamic equations that analyze key aspects of turbine performance, including temperature variations in turbine blades, angular velocities of rotating shafts, and mass–energy balances within the plenum and combustion chamber. Furthermore, we incorporate Kirchhoff's equation in its generalized conformable integral form, enhancing the precision of energy balance calculations and improving the representation of heat transfer processes in the combustion chamber. This methodology introduces novel perspectives in hydrogen turbine research, contributing to the advancement of sustainable and efficient technologies. Our comprehensive approach aims to provide more accurate and efficient predictions of turbine behavior, thereby impacting the design and optimization of hydrogen-based clean energy systems. [ABSTRACT FROM AUTHOR]