A remark on local fractional calculus and ordinary derivatives

TL;DR

This paper introduces a new general definition of local fractional derivatives involving an unknown kernel, linking it to ordinary derivatives and deriving fundamental properties for various kernel choices.

Contribution

It proposes a novel local fractional derivative framework dependent on an unknown kernel, unifying known cases and connecting to classical derivatives.

Findings

New general definition of local fractional derivative

Relation established between fractional and ordinary derivatives

Fundamental properties derived for different kernels

Abstract

In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.