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

TL;DR

This paper investigates the long-term behavior of solutions to space-time fractional PDEs with reaction terms, extending previous one-dimensional results to higher dimensions and broader fractional parameters using subordination techniques.

Contribution

It generalizes the understanding of the fundamental solution's invasion speed for fractional PDEs across multiple dimensions and fractional orders, employing subordination as a key method.

Findings

Extended invasion speed results to higher dimensions

Applicable to a wide range of fractional parameters

Used subordination to analyze asymptotic behavior

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.