On the equivalence of classical Helmholtz equation and fractional Helmholtz equation with arbitrary order

TL;DR

This paper demonstrates the equivalence between the classical Helmholtz equation and its fractional counterpart of arbitrary order, extending recent theoretical results in the field.

Contribution

It establishes a general equivalence between classical and fractional Helmholtz equations for any order, advancing the understanding of fractional differential equations.

Findings

Proves the equivalence for arbitrary fractional orders

Extends previous results by Guan, Murugan, and Wei

Provides a theoretical foundation for fractional Helmholtz equations

Abstract

We show the equivalence of the classical Helmoltz equation and the fractional Helmholtz equation with arbitrary order. This improves a recent result of Guan, Murugan and Wei \cite{gmw2022}