Constraints on cosmological models with gamma-ray bursts in cosmology-independent way

In this paper, we present a cosmology-independent method to constrain cosmological models from the latest 221 gamma-ray bursts (GRBs) sample, including 49 GRBs from Fermi catalog with the Amati relation (the [Formula: see text] correlation), which are calibrated by using a Gaussian process from the Pantheon+ type Ia supernovae (SNe Ia) sample. With 182 GRBs at [Formula: see text] in the Hubble diagram and the latest observational Hubble data (OHD) by the Markov Chain Monte Carlo (MCMC) method, we obtained [Formula: see text] and [Formula: see text] for the flat [Formula: see text]CDM model and [Formula: see text], [Formula: see text], [Formula: see text] for the flat wCDM model. These results are consistent with those in which the coefficients of the Amati relation and the cosmological parameters fitted simultaneously.