  In this paper, the thermodynamical properties and the phase transitions of
the charged accelerating anti-de Sitter (AdS) black holes are investigated in
the framework of the $f(R)$ gravity. By studying the conditions for the phase
transitions, it has been shown that the $P-V$ criticality and the van der Waals
like phase transitions can be achieved for $ T \approx T_{c} $. The
Joule-Thomson expansion effects are also examined for the charged accelerating
AdS black holes of the $f(R)$ gravity. Here, we derive the inversion
temperatures as well as the inversion curves. Then, we determine the position
of the reverse point for different values of mass $M$ and parameter $b$ for the
corresponding black hole. At this point, the Joule-Thompson coefficient is
zero. So, in such case, we can say that such point is very important for the
finding of cooling - heating regions. Finally, we calculate the ratio of
minimum inversion temperature and critical temperature for such black hole.
