  We address the problem of finding static and spherically symmetric
anisotropic compact stars in general relativity that admit conformal motions.
The study is framed in the language of f(R) gravity theory in order to expose
opportunity for further study in the more general theory. Exact solutions of
compact stars are found under the assumption that spherically symmetric
spacetimes which admits conformal motion with matter distribution anisotropic
in nature. In this work, two cases have been studied for the existence of such
solutions: first, we consider the model given by f(R) = R and then f(R) = aR+b.
Finally, specific characteristics and physical properties have been explored by
analytically along with graphical representations for conformally symmetric
compact stars in f(R) gravity.
