Left: least-square fit (dashed lines) of Eq. (10) to the local photon index (thick lines) in the keV-MeV range for the four time intervals of the synthetic burst GRB_B001. Right: least-square fit (dashed line) to the local photon index (solid line) in the keV-MeV range for several synthetic bursts: time integrated spectrum of two reference cases presented in BD14, case A (blue) and B (cyan) with a varying fraction of accelerated electrons and p = 2.7. Case A corresponds to the most standard fast cooling synchrotron spectrum, and case B to a modified synchrotron spectrum affected by inverse Compton scaterring in the Klein-Nishina regime. In addition, preliminary calculation of the same case B taking into account a magnetic field decay in the emission region are also presented (taken from Daigne & Bošnjak, in prep.) with a time scale of the decay (green) or 10⁻³ (red), where is the dynamical timescale. Finally, the same case is also shown for a time interval of 0.25 s around the peak of the light curve (magenta).