Alternative proposal to modified Newtonian dynamics

From a study of conserved quantities of the so-called modified Newtonian dynamics we propose an alternative to this theory. We show that this proposal is consistent with the Tully-Fisher law, has conserved quantities whose Newtonian limit are the energy and angular momentum, and can be useful to explain cosmic acceleration. The dynamics obtained suggests that, when acceleration is very small, time depends on acceleration. This result is analogous to that of special relativity where time depends on velocity.