  This article is devoted to investigate the effects of $f(R)$ theory in the
dynamics of a massless particle near the horizon of a static spherically
symmetric (SSS) black hole. Deriving the equations of motion within $f(R)$
gravitational theories, novel solutions for charged and neutral black holes are
obtained, introducing a dimensional parameter $a$ in $f(R)=R-2a\sqrt{R}$.
Departing from General Relativity, these solutions showcase unique properties
reliant on the dynamics of Ricci scalar. Analysis shows that chaos manifests
within a specific energy range, with $a$ playing a crucial role. The study
underscores the general applicability of the spherically symmetric metric,
revealing insights into particle dynamics near black hole horizons. Despite an
initially integrable nature, the introduction of harmonic perturbation leads to
chaos, aligning with the Kolmogorov-Arnold-Moser theory. This research
contributes to a nuanced understanding of black hole dynamics, emphasizing the
importance of alternative theories of gravity.
