  We propose a complete R-parity violating supersymmetric model with baryon
triality that contains a Dine-Fischler-Srednicki-Zhitnitsky axion chiral
superfield. We parametrize supersymmetry breaking with soft terms, and
determine under which conditions the model is cosmologically viable. As
expected we always find a region of parameter space in which the axion is a
cold dark matter candidate. The mass of the axino, the fermionic partner of the
axion, is controlled by a Yukawa coupling. When heavy [${\mathcal O}$(TeV)],
the axino decays early and poses no cosmological problems. When light
[$\mathcal{O}$(keV)] it can be long lived and a warm dark matter candidate. We
concentrate on the latter case and study in detail the decay modes of the
axino. We find that constraints from astrophysical X- and gamma rays on the
decay into photon and neutrino can set new bounds on some trilinear
supersymmetric R-parity violating Yukawa couplings. In some corners of the
parameter space the decays of a relic axino can also explain a putative 3.5 keV
line.
