Abstract

Our paper introduces a new theoretical framework called the Fractional Einstein-Gauss-Bonnet scalar field cosmology, which has important physical implications. Using fractional calculus to modify the gravitational action integral, we derived a modified Friedmann equation and a modified Klein-Gordon equation. Our research reveals non-trivial solutions associated with exponential potential, exponential couplings to the Gauss-Bonnet term, and a logarithmic scalar field, which are dependent on two cosmological parameters, m and alpha 0=t0H0 and the fractional derivative order mu. By employing linear stability theory, we reveal the phase space structure and analyze the dynamic effects of the Gauss-Bonnet couplings. The scaling behavior at some equilibrium points reveals that the geometric corrections in the coupling to the Gauss-Bonnet scalar can mimic the behavior of the dark sector in modified gravity. Using data from cosmic chronometers, type Ia supernovae, supermassive Black Hole Shadows, and strong gravitational lensing, we estimated the values of m and alpha 0, indicating that the solution is consistent with an accelerated expansion at late times with the values alpha 0=1.38 +/- 0.05, m=1.44 +/- 0.05, and mu=1.48 +/- 0.17 (consistent with Omega m,0=0.311 +/- 0.016 and h=0.712 +/- 0.007), resulting in an age of the Universe t0=19.0 +/- 0.7 [Gyr] at 1 sigma CL. Ultimately, we obtained late-time accelerating power-law solutions supported by the most recent cosmological data, and we proposed an alternative explanation for the origin of cosmic acceleration other than Lambda CDM. Our results generalize and significantly improve previous achievements in the literature, highlighting the practical implications of fractional calculus in cosmology.