Decay/growth rates for inhomogeneous heat equations with memory. The case of large dimensions

<abstract><p>We study the decay/growth rates in all $ L^p norms of solutions to an inhomogeneous nonlocal heat equation \mathbb{R}^N involving a Caputo \alpha $-time derivative and power \beta Laplacian when dimension is large, N > 4\beta $. Rates depend strongly on space-time scale time behavior spatial L^1 norm forcing term.</p></abstract>