Let \( n\in\mathbb N \), 0 < \( s \) < 1, \( n>2s \) and 1 < \( p \) < \( \frac{n+2s}{n-2s} \). We prove that every nonnegative classical entire solution of \( u_t+(-\Delta)^su=u^p\qquad\text{in }\mathbb{R}^n\times\mathbb{R} \) is identically zero. Our result extends the optimal Liouville theorem in [42] for the classical heat equation (\( s=1 \)) to the fractional cases 0 < \( s \) < 1 for the full range 1 < \( p \) < \( \frac{n+2s}{n-2s} \) without global boundedness, higher regularity or pointwise decay assumptions.