Fundamental Solutions and Decay of Fully Non-local Problems

TL;DR

This paper investigates a fully non-local reaction-diffusion equation in both time and space, constructing fundamental solutions via subordination and analyzing decay rates using harmonic analysis techniques.

Contribution

It introduces a novel approach to construct fundamental solutions for fully non-local equations and derives decay rates using harmonic analysis methods.

Findings

Constructed fundamental solutions for the non-local problem.

Derived decay rates for mild solutions.

Applied harmonic analysis to analyze temporal decay.

Abstract

In this paper, we study a fully non-local reaction-diffusion equation which is non-local both in time and space. We apply subordination principles to construct the fundamental solutions of this problem, which we use to find a representation of the mild solutions. Moreover, using techniques of Harmonic Analysis and Fourier Multipliers, we obtain the temporal decay rates for the mild solutions.