  In the present work, we study for the first time a scale--dependent
gravitational theory in a cosmological context in a matter--dominated era. In
particular, starting from the Einstein Hilbert action with cosmological
constant assuming scale--dependent couplings, we derive the corresponding
effective Friedmann equations for the model and we solve them. We analyse in
detail our results by comparing them with observational $\Lambda$CDM data as
well as the very well-known running vacuum models. Finally, we have provided,
in figures, the evolution of the Hubble parameter respect to the redshift as
well as the gravitational coupling respect to the Hubble parameter and they
show an agreement with the current observations.
