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Fractional cosmology modifies the standard derivative to Caputo’s fractional derivative of order μ, generating changes in General Relativity. Friedmann equations are modified, and the evolution of the species densities depends on μ and the age of the Universe tU. We estimate stringent constraints on μ using cosmic chronometers, Type Ia supernovae, and joint analysis. We obtain $\mu =2.839^{+0.117}_{-0.193}$ within the 1σ confidence level providing a non-standard cosmic acceleration at late times; consequently, the Universe would be older than the standard estimations. Additionally, we present a stability analysis for different μ values. This analysis identifies a late-time attractor corresponding to a power-law decelerated solution for μ < 2. Moreover, a non-relativistic critical point exists for μ > 1 and a sink for μ > 2. This solution is a decelerated power-law if 1 < μ < 2 and an accelerated power-law solution if μ > 2, consistent with the mean values obtained from the observational analysis. Therefore, for both flat FLRW and Bianchi I metrics, the modified Friedmann equations provide a late cosmic acceleration under this paradigm without introducing a dark energy component. This approach could be a new path to tackling unsolved cosmological problems.

Two results support the idea that the scalar and vector potentials in the Lorenz gauge can be considered to be physical quantities: (i) they separately satisfy the properties of causality and propagation at the speed of light and not imply spurious terms and (ii) they can naturally be written in a manifestly covariant form. In this paper we introduce expressions for the Lorenzgauge potentials at the present time in terms of electric and magnetic fields at the retarded time.These expressions provide a third result in favor of a physical interpretation of the Lorenz-gauge potentials: (iii) they can be regarded as causal effects of the observed electric and magnetic fields.