  We statistically examine the gamma-ray burst (GRB) photon indices obtained by
the Fermi-GBM and Fermi-LAT observations and compare the LAT GRB photon indices
to the GBM GRB photon indices. We apply the jitter radiation to explain the GRB
spectral diversities in the high-energy bands. In our model, the jitter
radiative spectral index is determined by the spectral index of the turbulence.
We classify GRBs into three classes depending on the shape of the GRB
high-energy spectrum when we compare the GBM and LAT detections: the GRB
spectrum is concave (GRBs turn out to be softer and are labeled as S-GRBs), the
GRB spectrum is convex (GRBs turn out to be harder and are labeled as H-GRBs),
and the GRBs have no strong spectral changes (labeled as N-GRBs). A universal
Kolmogorov index 7/3 in the turbulent cascade is consistent with the photon
index of the N-GRBs. The S-GRB spectra can be explained by the turbulent
cascade due to the kinetic magnetic reconnection with the spectral index range
of the turbulence from 8/3 to 3.0. The H-GRB spectra originate from the inverse
turbulent cascade with the spectral index range of the turbulence from 2.0 to
3.5 that occurred during the large lengthscale magnetic reconnection. Thus, the
GRB radiative spectra are diversified because the turbulent cascade modifies
the turbulent energy spectrum. More observational samples are expected in the
future to further identify our suggestions.
