  If dark matter particles are not perfectly stable, their decay products might
be seen in the cosmic-ray fluxes. A natural candidate for decaying dark matter
is the gravitino in R-parity violating scenarios. In the relevant GeV-TeV
energy range, the Fermi Large Area Telescope (LAT) is now measuring cosmic
gamma-ray fluxes with an unprecedented precision. We use the Fermi LAT
gamma-ray data to search for signatures from gravitino dark matter particles,
concentrating on gamma-ray lines and galaxy cluster observations. Implications
of our results for the decay length of the next-to-lightest superparticle,
which could be seen at the LHC in the near future, are discussed.
