  We present a sample of 74 Gamma-Ray Bursts (GRBs) from the Fermi-GBM
catalogue for which we compute the distance moduli and use them to constrain
effective dark energy models. To overcome the circularity problem affecting
GRBs as distance indicators, we calibrate the Amati relation of our sample with
a cosmology-independent technique. Specifically, we use the latest
observational Hubble parameter data, including associated systematics, to
approximate the cosmic expansion through a Bezier parametric curve. We
subsequently obtain the distance moduli of the GRBs and include the data in a
suite of recent cosmological observations of the expansion history (Planck
Compressed 2018, 2012 BOSS release of BAO data and Pantheon SNIa), to compute
Bayesian posterior constraints for the standard cosmological model
$\Lambda$CDM, as well as $\omega$CDM, and the CPL parametrization. Throughout
the analysis we strive to keep under control the error propagation and limit
our GRBs sample to avoid observational bias. As a result, we find no evidence
in favour of the alternatives to $\Lambda$CDM model. The latter agrees very
well with our calibrated sample of GRBs and presently available luminosity
distance probes.
