  We investigate a subdiffusive, fractional Fokker-Planck dynamics occurring in
time-varying potential landscapes and thereby disclose the failure of the
fractional Fokker-Planck equation (FFPE) in its commonly used form when
generalized in an {\it ad hoc} manner to time-dependent forces. A modified FFPE
(MFFPE) is rigorously derived, being valid for a family of dichotomously
alternating force-fields. This MFFPE is numerically validated for a rectangular
time-dependent force with zero average bias. For this case subdiffusion is
shown to become enhanced as compared to the force free case. We question,
however, the existence of any physically valid FFPE for arbitrary varying
time-dependent fields that differ from this dichotomous varying family.
