Dynamics of test particles and quasi-periodic oscillations mathematically around F(R)-corrected black holes

This study explores the influence of test particles in the vicinity of a static, spherically symmetric black hole (BH) within the $F\left(R\right)$-corrected model. The BH solution is illustrated by five parameters: mass M, three dimensionless coefficients a, b, and c, and the Planck length $l_p$. Using the effective potential, we show the stability of circular orbits and derive an exact result for the energy and angular momentum (AM) of particles in terms of the BH parameters. We define the innermost stable circular orbits (ISCOs) and examine the effective forces that influence particle trajectories. In addition, we analyze epicyclic oscillations (EO) close to the equatorial plane, providing exact formulas for radial, vertical, and orbital frequencies. The frequency of periastron precession is also evaluated. Furthermore, we investigate particle collisions near the BH horizon, computing the resulting center-of-mass energy (CME). Our results show the role of the model parameters in shaping the dynamics of the particles and their motion properties.