On a relativistic quark model description via the fractional Nikiforov–Uvarov method

Abstract

The Dirac equation (DE) plays an essential role in the relativistic quantum systems, which is reduced to a form similar to Schrödinger equation when a certain potential’s type is selected as the Cornell potential. By choosing the generalized fractional derivative, the fractional Nikiforov–Uvarov method is applied as a good efficient tool. The energy eigenvalues and corresponding wave functions are obtained in the sense of fractional forms by solving DE analytically. The special case is obtained, which is compatible with the classical model. In addition, we applied the present results on the light mesons such as [Formula: see text] and [Formula: see text]. Solving the fractional DE will open a new path to solve and improve results in the classical relativistic quantum systems.