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

We study the decay/growth rates in all Lp norms of solutions to an inhomogeneous nonlocal heat equation in RN involving a Caputo α-time derivative and a power β of the Laplacian when the dimension is large, N > 4β. Rates depend strongly on the space-time scale and on the time behavior of the spatial L1 norm of the forcing ter