Conformable fractional study of nuclear energy excitation by Bohr Hamiltonian with screened Kratzer potential for triaxial nuclei

In this work, we obtain new solutions of the Bohr Hamiltonian model appropriate for triaxial nuclei, with screened Kratzer potential in the framework of conformable fractional derivative. The analytical solutions for energy spectra are obtained using the conformable fractional Nikiforov–Uvarov method. We discuss the link between the present model and other relevant related models such as Z(5) model, classical screened Kratzer model and conformable fractional Kratzer model. The effect of the fractional-order parameter is investigated on the variations of the interaction potential. The normalized eigen-energies are calculated as well as normalized B(E2) transitions probabilities at different values of the fractional-order parameter. Our results reproduced well the experimental data for ${}^{126}$Xe, ${}^{128}$Xe, ${}^{130}$Xe, ${}^{192}$Pt, ${}^{194}$Pt and ${}^{196}$Pt atomic nuclei, and are found to be improved in comparison with other related theoretical models.