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In the present comment we discuss the qualitative and the quantitativedifferences between the neutron stars models in $f(R)$ gravity presented in therecent paper \cite{Capozziello2015} (Capozziello et al. (2015)) and in ourpaper \cite{Yazadjiev2014} (Yazadjiev et al. (2014)). The authors of\cite{Capozziello2015} claim that these differences come from the fact thatthey are using the physical Jordan frame while we are working in the Einsteinframe. The results in \cite{Yazadjiev2014} are very well tested by twonumerical codes using different formulations of the field equations that giveus the confidence that they are correct. Thus we decided to perform anadditional test. Namely, we derive the relevant set of field equations in theJordan frame and solve them numerically in order to disprove the claim in\cite{Capozziello2015} that the difference comes from the use of differentframe. The obtained results are in perfect agreement with our previous work\cite{Yazadjiev2014} and therefore the numerical results in\cite{Capozziello2015} seem to be incorrect. At the end we point out severalpossible sources of error in \cite{Capozziello2015} that can lead to theobserved large deviations.

Comment on "The Mass-Radius relation for Neutron Stars in $f(R)$ gravity" by S. Capozziello, M. De Laurentis, R. Farinelli and S. Odintsov