A nonlocal fractional Helmholtz equation

TL;DR

This paper investigates boundary value problems for a fractional Helmholtz equation with involution perturbation, establishing existence and uniqueness of solutions using spectral methods in a rectangular domain.

Contribution

It introduces a fractional analogue of the Helmholtz equation with involution perturbation and proves theorems on solution existence and uniqueness.

Findings

Existence of solutions is established.

Uniqueness of solutions is proved.

Spectral methods are effective for these fractional problems.

Abstract

In this paper we study some boundary value problems for a fractional analogue of second order elliptic equation with an involution perturbation in a rectangular domain. Theorems on existence and uniqueness of a solution of the considered problems are proved by spectral method.