Non-local Integrals and Derivatives on Fractal Sets with Applications

TL;DR

This paper explores non-local derivatives on fractal sets, specifically the Cantor set, analyzing their properties, solving related differential equations, and proposing physical models to illustrate their applications.

Contribution

It introduces the concept of non-local derivatives on fractals, providing scaling properties, solutions to fractal differential equations, and potential physical applications.

Findings

Derived scaling properties for fractal derivatives

Solved local and non-local fractal differential equations

Proposed physical models based on fractal derivatives

Abstract

In this paper, we discussed the non-local derivative on the fractal Cantor set. The scaling properties are given for both local and non-local fractal derivatives. The local and non-local fractal differential equations are solved and compared and related physical models are suggested.