New Derivatives for the Functions with the Fractal Tartan Support

TL;DR

This paper extends F-calculus to fractal Tartan spaces, enabling the calculation of derivatives and integrals on fractals with local properties suitable for physical modeling.

Contribution

It introduces a generalized fractional calculus framework for fractal Tartan spaces, expanding the tools available for analysis on complex fractal geometries.

Findings

Derived integral and derivative formulas for functions on fractal Tartan spaces.

Generalized fractional derivatives exhibit local properties beneficial for physical models.

Illustrative examples demonstrate the applicability of the new calculus.

Abstract

In this manuscript, we generalize F-calculus to apply it on fractal Tartan spaces. The generalized standard F-calculus is used to obtain the integral and derivative of the functions on the fractal Tartan with different dimensions. The generalized fractional derivatives have local properties that make it more useful in modelling physical problems. The illustrative examples are used to present the details.