Relativistic oscillators in the context of energy-dependent noncommutative phase space

In this work, we investigate the Klein-Gordon and Dirac oscillators in (2+1) dimensions under the influence of a constant magnetic field, within the framework of energy-dependent noncommutative phase space. This space is characterized by two energy-dependent deformation parameters, θ(E) and η(E), which modify the standard phase-space algebra through generalized commutation relations. By applying the Bopp shift method and using polar coordinates, we derive exact analytical solutions for both relativistic oscillators. The relativistic energy equations and corresponding wave functions are obtained explicitly in terms of confluent hypergeometric functions for the Klein-Gordon case and associated Laguerre functions for the Dirac case. We also analyze various limiting cases, including the commutative limit, the energy-independent NC case, and the non-relativistic regime. Our results show that the energy dependence of the noncommutative parameters leads to significant modifications in the spectral structure, potentially shedding light on quantum gravitational effects at high energies.