Abstract
Dirac equation with spatially or position-dependent mass and an attractive Coulomb-like field is constructed in Hausdorff dimension of order $$0<\alpha \le 1$$. The lower and upper components of the spinor wave function were derived in addition to the corresponding energy eigenvalues of the resulting relativistic equation. It was observed that, in Hausdorff radial dimension, the ground state energy of particles mass with spin half is enhanced which leads to an enhancement of electrons mass in agreement with recent theoretical observations and experimental data.
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