Estimated Age of the Universe in Fractional Cosmology

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 $0.9858\leq Ht<95.238$.