  Gamma-ray bursts (GRBs) are one of the most exciting sources that offer
valuable opportunities for investigating the evolution of energy fraction given
to magnetic fields and particles through microphysical parameters during
relativistic shocks. The delayed onset of GeV-TeV radiation from bursts
detected by the \textit{Fermi} Large Area Telescope (\textit{Fermi}-LAT) and
Cherenkov Telescopes provide crucial information in favor of the external-shock
model. Derivation of the closure relations (CRs) and the light curves in
external shocks requires knowledge of GRB afterglow physics. In this
manuscript, we derive the CRs and light curves in a stratified medium with
variations of microphysical parameters of the synchrotron and SSC afterglow
model radiated by an electron distribution with a hard and soft spectral index.
Using Markov Chain Monte Carlo simulations, we apply the current model to
investigate the evolution of the spectral and temporal indexes of those GRBs
reported in the Second Gamma-ray Burst Catalog (2FLGC), which comprises 29
bursts with photon energies above 10 GeV and of those bursts (GRB 180720B,
190114C, 190829A and 221009A) with energetic photons above 100 GeV, which can
hardly be modeled with the CRs of the standard synchrotron scenario. The
analysis shows that i) the most likely afterglow model using synchrotron and
SSC emission on the 2FLGC corresponds to the constant-density scenario, and ii)
variations of spectral (temporal) index keeping the temporal (spectral) index
constant could be associated with the evolution of microphysical parameters, as
exhibited in GRB 190829A and GRB 221009A.
