Power-Law Inflation in n-Dimensional Fractional Scalar Field Cosmology: Observational Constraints and Dynamical Analysis

Power-law inflation with $a(t)\propto t^m$ is conceptually simple and predicts a scalar tilt $n_s=1-2\mathrm{/}m$ compatible with CMB data, but in four-dimensional Einstein gravity it typically yields a tensor-to-scalar ratio $r=16\mathrm{/}m$ that is too large to satisfy current bounds. We show that a minimal extension based on fractional scalar-field cosmology resolves this tension. Introducing a fractional order $\alpha \mathrm{\ne }1$ generates non-local (memory) corrections in the Friedmann and Klein-Gordon dynamics that suppress $r$ while keeping $n_s$ essentially unchanged. We derive an explicit mapping $\alpha (n,m)$ and recover the standard power-law limit as $\alpha \to 1$. For observationally favored values $\alpha \approx 0.8$-$0.9$ in four dimensions we obtain $n_s\approx 0.965$ and $r\lesssim 0.04$, bringing power-law inflation into agreement with data. The scalar potential follows self-consistently as an exponential, and a dynamical-systems analysis shows the fractional power-law solutions form stable inflationary attractors over the viable parameter range. These results establish fractional power-law inflation as a predictive and testable framework, with clear targets for forthcoming CMB polarization measurements.