On the calculus of parameterized fractal curves

Abstract

In this paper, we apply $F^{\alpha}$-calculus on the fractal Koch and Ces\`{a}ro curves with different dimensions. A generalized Newton's second law on the fractal Koch and Ces\`{a}ro curves is given. Density of the moving particles absorbed on fractal Ces\`{a}ro are derived. Illustrative examples are given to present the details of $F^{\alpha}$-integrals and $F^{\alpha}$-derivatives.