  We consider $f(R)$ modified gravity with the chameleon mechanism as an
alternative approach to address the dark matter issue on the galactic scale.
Metric formalism of $f(R)$ theory is considered in this study. A mathematical
transformation tool called conformal transformation which transforms the action
from Jordan to Einstein frame is employed to simplify the fourth-order modified
field equation and to describe the extra degree of freedom $f_R$ by using a
minimally coupled scalar field (scalaron) showing the chameleonic character.
Then, we examine the viability of a newly introduced $f(R)$ gravity model on
behalf of the chameleonic behavior of the scalaron. The model analyzes this
behavior of the scalaron successfully with the singularity correction. Further,
we consider a test particle (star) in a static, spherically symmetric spacetime
to investigate the importance of the scalaron in galactic dynamics. In the
non-relativistic limit, the rotational velocity equation for the particle with
scalaron contribution is derived. This contribution is found to be model
dependent. We generate the rotation curves using the velocity equation and fit
the predicted curves to observational data of a set of thirty seven sample
galaxies of different categories. The curves are fitted based on two fitting
parameters $M_0$ and $r_c$. The fitting shows good agreement of the prediction
with the observed data.
