We present a leptonic model on the external shock framework to describe the long- and short- lasting GeV component of some GRBs. This model was already applied successfully to GRB 090926A, and we extend it to describe the high-energy emission of GRB 090902B and GRB 090510. We argue that the high-energy emission consists of two components, one at MeV energies with a duration of a few seconds during the prompt phase, and a second GeV component lasting hundred of seconds after the prompt phase. The short high-energy component can be described as SSC emission from a reverse shock and the longer component arises from SSC emission of the forward shock. The main assumption of our model is that the jet is magnetized and evolves in the thick-shell case. The calculated fluxes and break energies are all consistent with the observed values.
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