Electric quadrupole transitions of 98–112Ru atomic nuclei via conformable fractional Bohr Hamiltonian

In this paper, we investigate the energy spectra, wave functions and the [Formula: see text] transition rates for [Formula: see text]Ru atomic nuclei, using the conformable fractional Bohr Hamiltonian model. For the [Formula: see text]-part of the potential, the newly proposed Yukawa plus modified exponential potential is considered and the harmonic oscillator potential in [Formula: see text]-part, with [Formula: see text] fixed around [Formula: see text]. By using the conformable fractional Nikiforov–Uvarov method, energy spectra and wave functions are obtained analytically. The sensitivity of the potential parameters and the spectra with respect to the fractional order parameter is investigated. The normalized fractional energies and fractional electric quadrupole transition rates are compared with the available experimental predictions and those from existing theoretical studies. Comparisons are made at different values of the fractional derivative order. The results are presented across a broader range of values of [Formula: see text], providing a systematic analysis of how variations in this parameter influence the energy spectra, wave functions, and [Formula: see text] transition rates in Ru nuclei. Overall, the comparison of our results with experimental data shows the good accuracy of our model, especially when the fractional parameter goes to lower values. It can be concluded that the order of fractional derivative plays a crucial role in refining theoretical predictions of electric quadrupole transition rates, especially for transitions involving higher multipolarities.