# Diffusion on Fractal Ces\`aro Curve

## TL;DR

This paper extends calculus to fractal Koch and Cesàro curves, proposing a generalized Newton's law and analyzing particle density on these fractals with illustrative examples.

## Contribution

It introduces F-calculus on fractal curves and formulates a generalized Newton's second law specific to these fractals, providing new tools for fractal dynamics analysis.

## Key findings

- Derived particle density on fractal Cesàro curves.
- Presented detailed examples of F-integrals and F-derivatives.
- Proposed a generalized Newton's second law for fractal curves.

## Abstract

In this paper, we apply F-calculus on fractal Koch and Ces\`aro curves with different dimensions. Generalized Newton's second law on the fractal Koch and Ces\`aro curves is suggested. Density of moving particles which absorbed on fractal Ces\`aro are derived. More, illustrative examples are given to present the details of F-integrals and F-derivatives.