  We investigate entropic force cosmological models with the possibility of
matter creation and energy exchange between the bulk and the horizon of a
homogeneous and an isotropic flat Universe. We consider three different kinds
of entropy, Bekenstein's, the non-extensive Tsallis-Cirto's and the quartic
entropy, plus some phenomenological functional forms for matter creation rate
to model different entropic force models and put the observational constraints
on them. We show that while most of them are basically indistinguishable from a
standard $\Lambda$CDM scenario, the Bekenstein entropic force model with a
matter creation rate proportional to the Hubble parameter is statistically
highly favored over $\Lambda$CDM. As a general result, we also find that both
the Hawking temperature parameter $\gamma$, which relates the energy exchange
between the bulk and the boundary of the Universe, and the matter creation rate
$\Gamma(t)$, must be very small in order to reproduce observational data.
