Thermodynamic properties of heavy mesons in strongly coupled quark gluon plasma using the fractional of non-relativistic quark model

A generalized fractional derivative of the analytical exact iteration method is used, in which the two-body potential in strongly coupled quark–gluon plasma is devoted to solve the N -dimensional radial Schrödinger equation. The energy eigenvalues for any state ( n , l ) and mass spectra in the N -dimensional space have been investigated. The dissociation temperatures were computed in the N -dimensional space for different states of quarkonia. The effect of fractional-order parameter is investigated on the dissociation temperatures of heavy quarkonium masses such as charmonium and bottomonium and thermodynamic properties such as entropy, free energy, internal energy, and specific heat in the 3D and the higher-dimensional space. Also, the effect of dimensionality number on dissociation temperatures is discussed. A comparison with other recent works is displayed. We deduce that the fractional-order plays an essential role in 3D and higher-dimensional space.