Emergent inflation in fractional cosmology

In this paper, we investigate the evolution of the early universe within an emergent fractional cosmological framework. The underlying formulation is conceptually rooted in generalized measure constructions, closely related to fractal geometries and scale-dependent effective dimensions. By constructing a suitable fractional potential, we show that the cosmological evolution naturally originates from a non-singular pre-inflationary regime. Inflation arises dynamically without introducing an external scalar field and emerges as a stable attractor, exhibiting similarities with plateau-type inflationary scenarios. By analyzing the dynamical transition, we determine the end of inflation and establish a meaningful relation between the number of e-folds and the fractional parameter $\alpha$, ensuring consistency with observations and addressing the horizon problem. Moreover, the model admits a graceful exit from inflation, followed by an exact radiation-dominated solution with the standard time dependence and an $\alpha$-dependent normalization.