On the fractional quark–antiquark confinement and symplectic quantum mechanics

Using the formalism of generalized fractional derivatives, a two-dimensional nonrelativistic meson system is studied. The mesons are interacting by a Cornell potential. The system is formulated in the domain of the symplectic quantum mechanics by means of the generalized fractional Nikiforov–Uvarov method. The corresponding Wigner function and the energy eigenvalues are then derived. The effect of fractional parameters $\alpha$ and $\beta$ with the ground state solution is analyzed through the Wigner function for the charm–anticharm, bottom–antibottom and $b\overline{c}$ mesons. One of the fundamental achievements of such Cornell model is the determination of heavy quarkonia mass spectra. We have computed these masses and the present results are in agreement with the experimental data, improving previous theoretical results.