Energy states of the Hulthen plus Coulomb-like potential with position-dependent mass function in external magnetic fields

We need to solve a suitable exponential form of the position-dependent mass (PDM) Schr\"odinger equation with a charged particle placed in the Hulthen plus Coulomb-like potential field and under the influence of the external magnetic and Aharonov-Bohm (AB) flux fields. The bound state energies and their corresponding wave functions are calculated for spatially-dependent mass distribution function of a physical interest. A few plots of some numerical results to the energy are shown.