On a Leibnitz-type fractional derivative

TL;DR

This paper investigates a fractional derivative called the erivative, which obeys Leibniz rule, and explores its implications in analysis and differential geometry, revealing algebraic equivalence with traditional derivatives.

Contribution

It introduces and studies the erivative, a fractional derivative satisfying Leibniz rule, and examines its mathematical properties and implications.

Findings

erivative obeys Leibniz rule

It leads to a new scaling of the Leibniz derivative

All derivatives satisfying Leibniz rule are algebraically equivalent

Abstract

A type of fractional derivative, referred to as \alpha-derivative, is studied. The \alpha-derivative of fractional type obeys Leibnitz rule. Based on the definition of \alpha-derivative the operations of analysis and differential geometry are studied It was recently proved, that this variant of introduction of the derivative leads to a new scaling of the common Leibniz derivative, but not to a alternative type of derivation. In other words, all derivatives, that satisfy the Leibniz rule, are algebraically equivalent.