On the conformable fractional E(5) critical point symmetry

A new category of critical point symmetries is introduced. It is suggested that an element of this category, associated with zeros of conformable fractional Bessel functions, be utilized to describe spectra of nuclei around the E(5) critical point. The exact eigenvalue and eigenfunction solutions of local fractional Bohr-Mottelson Hamiltonian (with infinite square well potential) are obtained. The evolution of the spectra of the fractional E(5) critical point in correspondence with the fractional derivative order is investigated. Using the fractional E(5) critical point, a satisfactory description of the energy levels is obtained in the 102Pd and 104Ru nuclei.