On the existence of stationary solutions for certain systems of integro-differential equations with the double scale anomalous diffusion

TL;DR

This paper investigates the existence of solutions for a system of integro-differential equations modeling double scale anomalous diffusion, using fixed point methods and solvability conditions for non-Fredholm operators.

Contribution

It establishes the existence of solutions for complex integro-differential systems involving fractional Laplace operators with novel analytical techniques.

Findings

Proves existence of solutions under certain conditions.

Employs fixed point techniques in unbounded domains.

Addresses systems with fractional Laplacians in three dimensions.

Abstract

The work deals with establishing the solvability of a system of integro-differential equations in the situation of the double scale anomalous diffusion. Each equation of such system involves the sum of the two negative Laplace operators raised to two distinct fractional powers in the space of three dimensions. The proof of the existence of solutions is based on a fixed point technique. We use the solvability conditions for the non-Fredholm elliptic operators in unbounded domains.