Asymptotic profiles for inhomogeneous heat equations with memory

We study the large-time behavior in all L^p norms of solutions to an inhomogeneous nonlocal heat equation in ℝ^N involving a Caputo α -time derivative and a power β of the Laplacian when the dimension is large, N> 4β . The asymptotic profiles depend strongly on the space-time scale and on the time behavior of the spatial L^1 norm of the forcing term.