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The parametric Nikiforov-Uvarov (N-U) method is employed in conjunction witha generalized fractional derivative (GFD) to investigate the energy eigenvaluesand the total normalized wave function associated with the Coulomb plusscreened exponential hyperbolic potential (CPSEHP) in terms of Jacobipolynomials. This potential exhibits maximum effectiveness at lower values ofthe screening parameter. To explore the thermal and superstatisticalcharacteristics, the derived energy eigenvalues are directly incorporated intothe partition function (Z) and subsequently used to determine otherthermodynamic quantities, including vibrational mean energy (U), specific heatcapacity (C), entropy (S), and free energy (F). Comparisons with previousstudies are conducted. The classical case is recovered from the fractional caseby setting alpha = beta = 1, consistent with prior work. Our resultsdemonstrate that the fractional parameter plays a crucial role in governing thethermal and superstatistical properties within the framework of this model.

The Influence of Fractional Derivatives on Thermodynamic Properties by Studying the CPSEHP Interaction