The recently proposed conformable deformation of quantum mechanics by a fractional parameter $\alpha \in (0,1]$ has been used to construct a conformable quantum harmonic oscillator, which coincides with the standard quantum oscillator at $\alpha =1$. We argue that there is a conformable generalization of the uncertainty principle and use it to define the conformable coherent states of the conformable quantum oscillator along the general line of quantum mechanics. We investigate the fundamental physical and mathematical properties of these states in the $x^{\alpha }$-representation. In particular, we determine these states from the minimum uncertainty, compute their energy, find their conformable time-dependent form, determine the conformable translation operator, and show that conformable coherent states are eigenstates of the conformable annihilation operator. These states reproduce in the $\alpha =1$ limit of the correspondence principle the coherent states of the standard quantum harmonic oscillator.

We build a supersymmetric model with $SU{(3)}_C\otimes SU{(2)}_L\otimes U{(1)}_Y$ gauge symmetry, with a global ${{????}}_3\otimes (B-L)$ symmetry. The ${{????}}_3$ symmetry is necessary to keep the proton stable at least at tree level. There is also a global $(B-L)$ symmetry, where $(B)$ and $(L)$ are the usual baryonic and leptonic numbers, respectively. We introduce three nonidentical right-handed neutrinos plus new scalars fields. After symmetry breaking, the right-handed neutrinos together with one left-handed neutrino get Majorana masses via the seesaw mechanism. The other two left-handed neutrinos get their Majorana masses at 1-loop level. We will also explain the mixing angle in the neutrino sector in agreement with the experimental data and we get several interesting candidates to the observed dark matter.

We build a supersymmetric model based on the gauge group $SU{(3)}_C\otimes SU{(2)}_L\otimes U{(1)}_{Y^{\prime }}\otimes U{(1)}_{(B-L)}$ , where $Y^{\prime }$ is a new charge and $(B)$ and $(L)$ are the usual baryonic and leptonic numbers, respectively. The model has three right-handed neutrinos with nonidentical $(B-L)$ charges. The type-I seesaw mechanism is implemented for the generating masses for all the neutrinos. There are good candidates for dark matter and due to a Majorana phase at sneutrinos masses it is possible to induce leptogenesis in this model.

In this article, we give a brief review of the origin of the neutrino mass in some interesting non-linear supersymmetric models with R-symmetry. These models are able to address and solve the most important problems of particle physics and provide mechanisms for neutrino mass generation and their mixing parameters in agreement with the current experimental data. Their prediction could be experimentally tested in the near future by collider experiments.