On the calculus of parameterized fractal curves

Abstract

In this paper, we apply Fα -calculus on the fractal Koch and Cesaro curves with different dimensions. A generalized Newton's second law on the fractal Koch and Cesaro curves is given. Density of the moving particles absorbed on fractal Cesaro are derived. Illustrative examples are given to present the details of Fα -integrals and Fα -derivatives.