Phenomenological insights into holographically reconstructed fractional action cosmology: Cosmic dynamics, thermodynamics, and statefinder diagnostics

In this work, we use generalised infrared (IR) cutoffs as a reconstruction tool to investigate the dynamics of holographic dark energy through Fractional Action Cosmology (FAC). We construct a cosmological model that naturally takes into account important features like the universe's late-time acceleration by using fractional calculus to analyse the gravitational action. We investigate the energy conditions, thermodynamic behaviour, and equation of state (EoS) parameter in detail, with special attention to the Generalised Second Law (GSL). We discover that the model parameter n and the relaxation time τ both have important effects on cosmic evolution. According to statefinder diagnostics, the model fits the typical ΛCDM scenario quite well, but it also exhibits patterns that, in certain circumstances, resemble the behaviour of Chaplygin gas. Our findings demonstrate the FAC framework's adaptability and practicality in simulating cosmic evolution. Motivated by the Nojiri-Odintsov approach, we suggest expanding the current model to unify late-time acceleration and early-time inflation as a future direction. In order to gain a better understanding of phase transitions and to reinforce the cosmological significance of holographically reconstructed FAC, we also propose to generalize the IR cut-off to the Nojiri-Odintsov type.