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Our proposed cosmological framework, which is based on fractional quantumcosmology, aims to address the issue of synchronicity in the age of theuniverse. % Please check intended meaning is retained. To achieve this, we havedeveloped a new fractional $\Lambda$CDM cosmological model. We obtained thenecessary formalism by obtaining the fractional Hamiltonian constraint in ageneral minisuperspace. This formalism has allowed us to derive the fractionalFriedmann and Raychaudhuri equations for a homogeneous and isotropic cosmology.Unlike the traditional de Sitter phase, our model exhibits a power-lawaccelerated expansion in the late-time universe, when vacuum energy becomesdominant. % Please check intended meaning is retained. By fitting the model'sparameters to cosmological observations, we determined that the fractionalparameter of L\'{e}vy equals $\alpha=1.986$. Additionally, we have calculatedthe age of the universe to be 13.8196 Gyr. Furthermore, we have found that theratio of the age to Hubble time from the present epoch to the distant future isfinite and confined within the interval $0.9858\leq Ht<95.238$.

Estimated Age of the Universe in Fractional Cosmology