  We investigate numerically $f(R)$ gravity effects on certain AdS/CFT tools
including holographic entanglement entropy and two-point correlation functions
for a charged single accelerated Anti-de Sitter black hole in four dimensions.
We find that both holographic entanglement entropy and two-point correlation
functions decrease by increasing acceleration parameter $A$, matching perfectly
with literature. Taking into account the $f(R)$ gravity parameter $\eta$, the
decreasing scheme of the holographic quantities persist. However, we observe a
transition-like point where the behavior of the holographic tools change. Two
regions meeting at such a transit-like point are shown up. In such a
nomination, the first one is associated with slow accelerating black holes
while the second one corresponds to a fast accelerating solution. In the first
region, the holographic entanglement entropy and two-point correlation
functions decrease by increasing the $\eta$ parameter. However, the behavioral
situation is reversed in the second one. Moreover, a cross-comparison between
the entropy and the holographic entanglement entropy is presented providing
another counter-example showing that such two quantities do not exhibit similar
behaviors.
