Non-local Integrals and Derivatives on Fractal Sets with Applications

Abstract

In this paper, we discuss non-local derivatives on fractal Cantor sets. 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. Related physical models are also suggested.

Keywords

• fractal calculus
• non-local fractal derivatives
• scale change
• cantor set
• fractal dimension
• 05.45.df
• 47.53.+n