arXiv subjects

Mohammed K. A. Kaabar

Publications and source records attributed to Mohammed K. A. Kaabar.

2 recordsLinked to original sources

arXiv2023

On a Relativistic Quark Model Description via the Fractional Nikiforov-Uvarov Method

The Dirac equation plays an essential role in the relativistic quantum systems, which is reduced to a form similar to Schrodinger 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 Dirac equation analytically. The special case is obtained, which is compatible with the classical model. Solving the fractional Dirac equation will open a new path to solve and improve results in the classical relativistic quantum systems.

hep-ph↗

arXiv2020

New approximate-analytical solutions for the nonlinear fractional Schrödinger equation with second-order spatio-temporal dispersion via double Laplace transform method

In this paper, a modified nonlinear Schrödinger equation with spatio-temporal dispersion is formulated in the senses of Caputo fractional derivative and conformable derivative. A new generalized double Laplace transform coupled with Adomian decomposition method has been defined and applied to solve the newly formulated nonlinear Schrödinger equation with spatio-temporal dispersion. The approximate analytical solutions using the proposed generalized method in the sense of Caputo fractional derivative and conformable derivatives are obtained and compared with each other graphically.

math.GM↗