Inverse-power potentials with positive-bound energy spectrum from fractal, extended uncertainty principle and position-dependent mass arguments

In this study, we have introduced a new generalized momentum operator which takes simultaneously into account the extended uncertainty principle, the concept of position-dependent mass and fractal gradient arguments. The associated Schrodinger equation is obtained and analyzed for the case of potentials characterized by inverse-power terms with arbitrary strengths. It was observed that, in contrast to what is obtained in the literature, the corresponding quantum systems are characterized by positive-bound energy spectrum similar to what occurred in quasiparticles theory in condensed matter physics.