Local Fractional Calculus currently. A Mosaic of Definitions and the Quest for Unification

TL;DR

This paper reviews the development of local fractional calculus, highlighting the diversity of definitions and exploring the possibility of unifying this rapidly evolving mathematical field.

Contribution

It provides an overview of various local fractional calculus definitions and discusses the ongoing quest for a unified theoretical framework.

Findings

Diverse definitions of local fractional calculus are currently in use.

There is an active effort to develop a unifying formulation.

The field is rapidly evolving with ongoing consolidation efforts.

Abstract

In this paper, we present an overview of the development of one of the most dynamic areas of mathematics today: local differential operators of non-integer order. The underlying question is whether we are witnessing a period of consolidation and are on the way to a general formulation of this fascinating topic.