  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.
