Higher order fractional derivatives

TL;DR

This paper introduces a new fractional derivative generalization based on the Liouville-Weyl definition, unifying higher order derivatives with Riesz and Feller derivatives as special cases.

Contribution

It presents a novel direct fractional generalization of higher order derivatives, expanding the theoretical framework of fractional calculus.

Findings

Riesz and Feller derivatives are special cases of the new approach

The new definition generalizes higher order derivatives in fractional calculus

Provides a unified framework for various fractional derivatives

Abstract

Based on the Liouville-Weyl definition of the fractional derivative, a new direct fractional generalization of higher order derivatives is presented. It is shown, that the Riesz and Feller derivatives are special cases of this approach.