On the calculus of parameterized fractal curves

Authors: ALIREZA KHALILI GOLMANKANEH

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.

Keywords: $F^{\alpha}$-calculus, fractal Koch curve, staircase function; fractal Ces\`{a}ro curve,

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