Observational constraints on QPOs with orbital motion around charged non-commutative Schwarzschild black hole surrounded by perfect fluid dark matter

We study the orbital and oscillatory motion of test particles around a charged, non-commutative black hole surrounded by perfect fluid dark matter. We derive analytical expressions for the radial profiles of specific energy and angular momentum of stable equatorial circular orbits and discuss their stability using the effective potential approach. We also analyze the innermost stable circular orbits, the effective force acting on particles, and the frequencies of radial and latitudinal harmonic oscillations. The paper explores the quasi-periodic oscillations of particles near stable orbits and addresses periastron precession. We find that the model parameters strongly influence the motion of particles around black holes. Using observational data from multiple X-ray binary structures, we apply Monte Carlo Markov Chain (MCMC) analyses to restrain certain parameters such as α, β, and Q corresponding to the considered black hole.