  We present broadband (radio, optical, X-ray and GeV) fits to the afterglow
light curves and spectra of three long-duration gamma-ray bursts (GRBs 080916C,
090902B, and 090926A) detected by the Gamma-Ray Burst Monitor (GBM) and Large
Area Telescope (LAT) instruments on the Fermi satellite. Using the observed
broadband data, we study the origin of the high energy emission, and suggest
that the early-time GeV emission and the late-time radio, optical, and X-ray
afterglows can be understood as being due to synchrotron emission from an
external forward shock caused by structured ejecta propagating in a wind bubble
jumping to a homogeneous density medium. If the ceasing time for majority of
the energy injection is assumed to be close to the deceleration time of the
forward shock, the structured ejecta with continuous energy injection to the
forward shock can well explain the early rising feature of the GeV mission from
these burst, and the density-jump medium can account for some certain plateaus
or flares in the late afterglows. From our fits, we find that, on one hand, the
external shock origin of the GeV photons will make the optical depth have not
significant contribution to the early LAT rising part, which will loosen strong
constraint of lower limits of Lorentz factor. On the other hand, these
Fermi-LAT events preferentially occur in a low-density circumburst environment,
in which case the Klein-Nishina cutoff will significantly suppress the
Self-Synchrotron Compton (SSC) radiation. Such an environment might result from
superbubbles or low-metallicity progenitor stars (which have a low mass-loss
rate at late times of stellar evolution) of type Ib/c supernovae.
