The Parametric Generalized Fractional Nikiforov-Uvarov Method and Its Applications

TL;DR

This paper introduces a parametric generalized fractional Nikiforov-Uvarov method using fractional derivatives to exactly solve second-order differential equations, with applications to various potentials in molecular and hadron physics.

Contribution

It develops a novel fractional differential equation solving method and applies it to multiple important physical potentials, extending classical results.

Findings

Exact solutions for various potentials in fractional form.

Reduction to classical cases when fractional parameters equal one.

Agreement with recent classical results.

Abstract

By using generalized fractional derivative, the parametric generalized fractional Nikiforov-Uvarov (NU) method is introduced. The second-order parametric generalized differential equation is exactly solved in the fractional form. The obtained results are applied on the extended Cornell potential, the pesudoharmonic potential, the Mie potential, the Kratzer-Fues potential, the harmonic oscillator potential, the Morse potential, the Woods-Saxon potential, the Hulthen potential, the deformed Rosen-Morse potential and the Poschl-Teller potential which play an important role in the fields of molecular and hadron physics. The special classical cases are obtained from the fractional cases at ELFA = BETA =1 which are agreements with recent works.