Uniqueness of the fractional derivative definition

TL;DR

This paper introduces new local differential representations of the Riesz fractional derivative and discusses their implications for solving the fractional Schrödinger equation, expanding understanding of fractional derivatives.

Contribution

It presents two novel differential forms of the Riesz fractional derivative that highlight local properties, differing from the traditional integral form.

Findings

New differential representations emphasize local aspects of the fractional derivative

Implications for solutions of the fractional Schrödinger equation are discussed

Enhances understanding of the uniqueness of fractional derivative definitions

Abstract

For the Riesz fractional derivative besides the well known integral representation two new differential representations are presented, which emphasize the local aspects of a fractional derivative. The consequences for a valid solution of the fractional Schroedinger equation are discussed.