  We analyse the $f(R)$ gravity in the so-called Jordan frame, as implemented
to the isotropic Universe dynamics. The goal of the present study is to show
that, according to recent data analyses of the supernovae Ia Pantheon sample,
it is possible to account for an effective redshift dependence of the Hubble
constant. This is achieved via the dynamics of a non-minimally coupled scalar
field, as it emerges in the $f(R)$ gravity. We face the question both from an
analytical and purely numerical point of view, following the same technical
paradigm. We arrive to establish that the expected decay of the Hubble constant
with the redshift $z$ is ensured by a form of the scalar field potential, which
remains essentially constant for $z\lesssim0.3$, independently if this request
is made a priori, as in the analytical approach, or obtained a posteriori, when
the numerical procedure is addressed. Thus, we demonstrate that an $f(R)$ dark
energy model is able to account for an apparent variation of the Hubble
constant due to the rescaling of the Einstein constant by the $f(R)$ scalar
mode.
