In the present paper an attempt is made to develop a fractional integral and differen- tial, deterministic and projective method based on the assumption of the essential discontinuity observed in real systems (note that more than 99% of the volume occupied by an atom in real space has no matter). The differential treatment assumes continuous behaviour (in the form of averaging over the recent past of the system) to predict the future time evolution, such that the real history of the system is “forgotten”. So it is easy to understand how problems such as unpredictability (chaos) arise for many dynamical systems, as well as the great difficulty to connecting Quantum Mechanics (a probabilistic differential theory) with General Relativity (a deterministic differential theory). I focus here on showing how the present theory can throw light on crucial astrophysical problems like dark matter and dark energy