  We consider work fluctuation relations (FRs) for generic types of dynamics
generating anomalous diffusion: Levy flights, long-correlated Gaussian
processes and time-fractional kinetics. By combining Langevin and kinetic
approaches we calculate the probability distributions of mechanical and
thermodynamical work in two paradigmatic nonequilibrium situations,
respectively: a particle subject to a constant force and a particle in a
harmonic potential dragged by a constant force. We check the transient FR for
two models exhibiting superdiffusion, where a fluctuation-dissipation relation
does not exist, and for two other models displaying subdiffusion, where there
is a fluctuation-dissipation relation. In the two former cases the conventional
transient FR is not recovered, whereas in the latter two it holds either
exactly or in the long-time limit.
