Asymptotic behavior of the fundamental solution of space-time fractional equations with a reaction term

Abstract

In this paper, we consider a space-time fractional partial differential equation with a reactive term. We describe the speed of invasion of its fundamental solution, extending recent results in this topic, which had been proved for the one dimensional spatial setting and some fractional parameters involved in the equation. The key tool to achieve these results in a wide range of cases (any spatial dimension, any time and spatial fractional differential parameters, and any polynomial speed of invasion) is the subordination.