Anomalous cyclic in the neutrino oscillations

Neutrino physics is one of the most important topics in particle physics and cosmology. As it is known, neutrinos are weakly interacting fundamental particles with chargeless and very small masses. One of the most characteristic features of the neutrino that make a difference from other elementary particles is that it oscillates between the mass and flavour eigenstates. Due to these oscillations, neutrinos change from one flavour to another. So far in theory the possible effects of deformed space-time effects on oscillation have not been considered. In this study, we show for the first time that a deformed space-time metric will lead to fractional dynamics between mass and flavour changes and therefore cause a phase shift in the oscillation period. We also shortly discuss the possible relation between anomalous cyclic and relic neutrinos. The modification in the oscillation probabilities due to the studied effect in this work could be seen using relic neutrinos.