Investigating heavy quarkonia binding in an anisotropic-dense quark-gluon plasma with topological defects in the framework of fractional non-relativistic quark model.

The quark-gluon plasma analysis relies on the heavy quark potential, which is influenced by the anisotropic plasma parameter temperature (t), and baryonic chemical potential (μ). Employing the generalized fractional derivative Nikiforov-Uvarov (GFD-NU) method, we solved the topologically-fractional Schrödinger equation. Two scenarios were explored: the classical model (α = β = 1) and the fractional model (α, β < 1).

A precise estimation for vibrational energies of diatomic molecules using the improved Rosen-Morse potential.

In the context of the generalized fractional derivative, novel solutions to the D-dimensional Schrödinger equation are investigated via the improved Rosen-Morse potential (IRMP). By applying the Pekeris-type approximation to the centrifugal term, the generalized fractional Nikiforov-Uvarov method has been used to derive the analytical formulations of the energy eigenvalues and wave functions in terms of the fractional parameters in D-dimensions. The resulting solutions are employed for a variety of diatomic molecules (DMs), which have numerous uses in many fields of physics.

The generalized fractional NU method for the diatomic molecules in the Deng-Fan model.

Abstract: A solution of the fractional -dimensional radial Schrödinger equation (SE) with the Deng-Fan potential (DFP) is investigated by the generalized fractional Nikiforov-Uvarov (NU) method. The analytical formulas of energy eigenvalues and corresponding eigenfunctions for the DFP are generated. Furthermore, the current results are applied to several diatomic molecules (DMs) for the DFP as well as the shifted Deng-Fan potential (SDFP).

A Novel Computational Tool for the Fractional-Order Special Functions Arising from Modeling Scientific Phenomena via Abu-Shady-Kaabar Fractional Derivative.

Recently, a generalized fractional derivative formulation, known as Abu-Shady-Kaabar fractional derivative, is studied in detail which produces satisfactory results that are consistent with conventional definitions of fractional derivative such as Caputo and Riemann-Liouville. To derive the fractional forms of special functions, the generalized fractional derivative is used. The findings demonstrate that the current findings are compatible with Caputo findings.