  In this paper some of the brightest GeV sources observed by the Fermi-LAT
were analysed, focusing on their spectral cut-off region. The sources chosen
for this investigation were the brightest blazar flares of 3C~454.3 and 3C~279
and the Vela pulsar with a reanalysis with the latest Fermi-LAT software. For
the study of the spectral cut-off we first explored the Vela pulsar spectrum,
whose statistics in the time interval of the 3FGL catalog allowed strong
constraints to be obtained on the parameters. We subsequently performed a new
analysis of the flaring blazar SEDs. For these sources we obtained constraints
on the cut-off parameters under the assumption that their underlying spectral
distribution is described by a power-law with a stretched exponential cut-off.
We then highlighted the significant potential improvements on such constraints
by observations with next generation ground based Cherenkov telescopes,
represented in our study by the Cherenkov Telescope Array (CTA). Adopting
currently available simulations for this future observatory, we demonstrate the
considerable improvement in cut-off constraints achievable by observations with
this new instrument when compared with that achievable by satellite
observations.

High Energy Astrophysical Phenomena