  Our proposed cosmological framework, which is based on fractional quantum
cosmology, aims to address the issue of synchronicity in the age of the
universe. To achieve this, we have developed a new fractional $\Lambda$CDM
cosmological model. We obtained the necessary formalism by obtaining the
fractional Hamiltonian constraint in a general minisuperspace. This formalism
has allowed us to derive the fractional Friedmann and Raychaudhuri equations
for a homogeneous and isotropic cosmology. Unlike the traditional de Sitter
phase, our model exhibits a power-law accelerated expansion in the late-time
universe, when vacuum energy becomes dominant. By fitting the model's
parameters to cosmological observations, we determined that the fractional
parameter of L\'{e}vy equals $\alpha=1.986$. Additionally, we have calculated
the age of the universe to be 13.8196 Gyr. Furthermore, we have found that the
ratio of the age to Hubble time from the present epoch to the distant future is
finite and confined within the interval $0.9858\leq Ht<95.238$.
