  In this study, we investigated the impact of a topological defect on the
properties of heavy quarkonia using the extended Cornell potential. We solved
the fractional radial Schrodinger equation (SE) using the extended
Nikorov-Uvarov (ENU) method to obtain the eigen energy, which allowed us to
calculate the masses of charmonium and bottomonium. One significant observation
was the splitting between np and nd states, which we attributed to the presence
of the topological defect. We discovered that the excited states were divided
into components corresponding to 2l + 1, indicating that the gravity field
induced by the topological defect interacts with energy levels in a manner
similar to the Zeeman effect caused by a magnetic field. Additionally, we
derived the wave function and calculated the root mean radii for charmonium and
bottomonium. A comparison with classical models was performed, resulting in
better results being obtained. Furthermore, we investigated the thermodynamic
properties of charmonium and bottomonium, determining quantities such as
energy, partition function, free energy, mean energy, and specific heat for
p-states. The obtained results were found to be consistent with experimental
data and previous works. In conclusion, the fractional model used in this work
proved essential in understanding the various properties and behaviors of heavy
quarkonia in the presence of topological defects.
