  Anomalous dynamics characterized by non-Gaussian probability distributions
(PDFs) and/or temporal long-range correlations can cause subtle modifications
of conventional fluctuation relations. As prototypes we study three variants of
a generic time-fractional Fokker-Planck equation with constant force. Type A
generates superdiffusion, type B subdiffusion and type C both super- and
subdiffusion depending on parameter variation. Furthermore type C obeys a
fluctuation-dissipation relation whereas A and B do not. We calculate
analytically the position PDFs for all three cases and explore numerically
their strongly non-Gaussian shapes. While for type C we obtain the conventional
transient work fluctuation relation, type A and type B both yield deviations by
featuring a coefficient that depends on time and by a nonlinear dependence on
the work. We discuss possible applications of these types of dynamics and
fluctuation relations to experiments.
