  New approximate analytical solutions have been obtained for the conformable
fractional collective Bohr Hamiltonian suitable for triaxial nuclei, with the
harmonic oscillator in {\gamma}-part of the collective potential and different
exponential-type potentials (namely Morse, Tietz-Hua, and multi-parameter
exponential-type potential) in \b{eta}-part. The conformable fractional
Nikiforov-Uvarov approach is used to derive closed analytical formulas for
energy spectra and wave functions. The relation between the conformable
fractional spectra of the three potentials and the Z(5) spectrum has been
studied. The evolution of the energy spectra as a function of the potential
parameters has been investigated for the three potentials. The normalized B(E2)
transition rates and spectra have been calculated and compared with the
experimental data and theoretical predictions of Kratzer potential. The
predictions can describe well the experimental results for 114,116Pd,
126,128Xe, and 192,194Pt isotopes.
