This paper investigates the cosmological transition epoch when dark energy begins to dominate over matter, using gamma-ray burst (GRB) correlations and cosmographic methods. The study employs two model-independent approaches: the direct expansion of the Hubble rate (DHE) and the direct expansion of the deceleration parameter (DDPE). These methods allow for the determination of the transition redshift $ z_t $ and the jerk parameter $ j_t $, which describe the expansion history of the universe. The researchers use four GRB correlations—Amati, Combo, Yonetoku, and Dainotti—along with type Ia supernovae (SNe Ia) and baryonic acoustic oscillations (BAO) to constrain cosmological parameters. The GRB correlations are calibrated using Bézier interpolation of updated Hubble data to avoid the circularity problem. A Monte Carlo Markov Chain (MCMC) analysis is performed to estimate the parameters of the DHE and DDPE models and the GRB correlations. The results are consistent with the concordance model ($ \Lambda $CDM), with some exceptions. The dark energy behavior is analyzed, and its compatibility with a cosmological constant is verified. The matter density $ \Omega_m $ is constrained and compared with the concordance model predictions. The study finds that the dark energy evolution is very slow and almost indistinguishable from the case of a cosmological constant. The transition redshift $ z_t $ is found to be compatible with the concordance model, with the $ L_0-E_p-T $ correlation providing the closest value. The jerk parameter $ j_t $ is found to be compatible with $ j = 1 $, consistent with the $ \Lambda $CDM model. The results from both DHE and DDPE methods are in agreement with the concordance model, confirming that dark energy behaves as a cosmological constant. The study concludes that the dark energy evolution is very slow and indistinguishable from the case of a cosmological constant. The results are consistent with the concordance model, and the matter density $ \Omega_m $ is found to be compatible with the Planck Collaboration's value. The study also highlights the importance of using model-independent methods to analyze cosmological data and avoid circularity issues.This paper investigates the cosmological transition epoch when dark energy begins to dominate over matter, using gamma-ray burst (GRB) correlations and cosmographic methods. The study employs two model-independent approaches: the direct expansion of the Hubble rate (DHE) and the direct expansion of the deceleration parameter (DDPE). These methods allow for the determination of the transition redshift $ z_t $ and the jerk parameter $ j_t $, which describe the expansion history of the universe. The researchers use four GRB correlations—Amati, Combo, Yonetoku, and Dainotti—along with type Ia supernovae (SNe Ia) and baryonic acoustic oscillations (BAO) to constrain cosmological parameters. The GRB correlations are calibrated using Bézier interpolation of updated Hubble data to avoid the circularity problem. A Monte Carlo Markov Chain (MCMC) analysis is performed to estimate the parameters of the DHE and DDPE models and the GRB correlations. The results are consistent with the concordance model ($ \Lambda $CDM), with some exceptions. The dark energy behavior is analyzed, and its compatibility with a cosmological constant is verified. The matter density $ \Omega_m $ is constrained and compared with the concordance model predictions. The study finds that the dark energy evolution is very slow and almost indistinguishable from the case of a cosmological constant. The transition redshift $ z_t $ is found to be compatible with the concordance model, with the $ L_0-E_p-T $ correlation providing the closest value. The jerk parameter $ j_t $ is found to be compatible with $ j = 1 $, consistent with the $ \Lambda $CDM model. The results from both DHE and DDPE methods are in agreement with the concordance model, confirming that dark energy behaves as a cosmological constant. The study concludes that the dark energy evolution is very slow and indistinguishable from the case of a cosmological constant. The results are consistent with the concordance model, and the matter density $ \Omega_m $ is found to be compatible with the Planck Collaboration's value. The study also highlights the importance of using model-independent methods to analyze cosmological data and avoid circularity issues.