Emergent Inflation in Fractional Cosmology

We investigate the dynamics of the early universe within an emergent fractional cosmological framework generated by a measure-deformed Newtonian action, without introducing additional propagating degrees of freedom. Considering asymptotic and dynamical requirements, we construct a minimal fractional potential that, together with the time-dependent fractional kernel, generates a regular pre-inflationary stage, quasi-de Sitter inflation, a dynamically controlled exit, and a subsequent finite duration radiation-like phase. The exact solution of the reduced early-time equation is obtained in two equivalent representations, and regularity selects a unique physical branch with finite principal curvature invariants at the initial boundary. Remarkably, the same exact trajectory evolves asymptotically toward the quasi-de Sitter regime, while an exact nonlinear analysis of homogeneous Hubble deviations establishes its asymptotic attractor character within the admissible expanding sector. Inflation ends dynamically near the zero crossing of the effective fractional force, leading to controlled background-level consistency relations among the inflationary duration, the fractional parameter, the effective equation of state parameter, and the exit scale. For the physically relevant post-inflationary regime, the model admits the characteristic radiation-like expansion over a finite post-inflationary interval. These results show that a coherent sequence of regular pre-inflationary, inflationary, and post-inflationary background dynamics can emerge from a simple and unified fractional Newtonian framework without invoking an inflaton field.