By applying the generalized fractional-Nikiforov-Uvarov approach, the radial Schrodinger equation is analytically solved in the longitudinal–traverse plane. The energy eigenvalues and associated functions are calculated by extending the interaction potential to an anisotropic hot-dense quark-gluon plasma medium. For heavy quarkonium masses like charmonium and bottomonium, the special cases of the mass of quarkonium are obtained at α = β = 1. The effect of the fraction parameter is investigated within the context of the quark-gluon plasma medium on the binding energy and dissociation temperature when baryonic chemical potential is included. A comparison are studoed with recent works Therefore, the fractional quark model correctly represents heavy mesons in an anisotropic hot-dense quark-gluon plasma medium, according to the current findings.
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