Asymptotic behavior of solutions to space-time fractional diffusion equations

Abstract

This article discusses the analyticity and the long-time asymptotic behavior of solutions to space-time fractional diffusion equations in ${\mathbb{R}}^d$. By a Laplace transform argument, we prove that the decay rate of the solution as $t\to \infty$ is dominated by the order of the time-fractional derivative. We consider the decay rate also in a bounded domain.