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

Abstract: The parametric Nikiforov-Uvarov (N-U) method is employed in conjunction with a generalized fractional derivative (GFD) to investigate the energy eigenvalues and the total normalized wave function associated with the Coulomb plus screened exponential hyperbolic potential (CPSEHP) in terms of Jacobi polynomials. This potential exhibits maximum effectiveness at lower values of the screening parameter. To explore the thermal and superstatistical characteristics, the derived energy eigenvalues are directly incorporated into the partition function (Z) and subsequently used to determine other thermodynamic quantities, including vibrational mean energy (U), specific heat capacity (C), entropy (S), and free energy (F). Comparisons with previous studies are conducted. The classical case is recovered from the fractional case by setting alpha = beta = 1, consistent with prior work. Our results demonstrate that the fractional parameter plays a crucial role in governing the thermal and superstatistical properties within the framework of this model.