Thermodynamic analysis and mass spectra of heavy mesons via the generalized fractional Klein-Gordon equation

By employing the generalized fractional Nikiforov-Uvarov (GF-NU) method, we successfully derive solutions of the generalized fractional Klein-Gordon (GF-KG) equation for both the screened Kratzer and a specific class of Yukawa potentials. These solutions yield the generalized fractional energy eigenvalues across both the relativistic and non-relativistic domains. Furthermore, the corresponding generalized fractional eigenfunctions can be obtained. We employed the derived solutions to calculate the heavy-meson masses of Charmonium (cc) and Bottomonium (bb), along with those of heavy-light mesons (cs, cq, bs, bq). Notably, the Charmonium and Bottomonium masses were plotted as functions of the orbital and angular quantum numbers, reduced mass, and fractional parameter. Similarly, the heavy-light meson masses were plotted in relation to their orbital and angular quantum numbers. Additionally, a thermodynamic analysis of the heavy-light mesons was conducted. The obtained results demonstrate a high degree of concordance with established experimental data and the findings of other researchers