Relativistic energy spectra of diatomic molecules through the solutions of general conformable fractional (GCF) Klein-Gordon equation for Hulthen potential with position-dependent mass (PDM) and the thermodynamic properties

In this study, we investigate the thermodynamic properties of some diatomic molecules modelled by Hulthen potential with PDM. The GCF Klein-Gordon equation in the GCF cylindrical coordinate for the Hulthen potential and the PDM function is solved by using the GCF Laplace method to obtain the GCF energy equation and GCF wave function. The effect of the fractional order, quantum number, potential parameter, and PDM parameter on the energy eigenvalue of the H-2, LiH, and HF diatomic molecules is discussed through the corresponding graphs computed using MATLAB software. The results show that the fractional order, quantum number, and potential parameter cause the energy spectrum to increase. In addition, the thermodynamic properties are examined by calculating the partition function. Based on the results, internal energy tends to be constant at lower temperatures, and the specific heat capacity decreases with increasing beta . Whereas free energy and entropy increase monotonically with increasing beta. To validate our findings, we compare our results with those obtained in the literature.