Abstract
In this paper, we summarize fractal calculus on fractal curves and nonstandard analysis. Using nonstandard analysis which includes hyperreal and hyperinteger numbers, we define left and right limits and derivatives on fractal curves. Fractal integral and differential forms are defined using nonstandard analysis. Some examples are solved to show details.
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Cristina Serpa acknowledges partial funding by national funds through FCT-Foundation for Science and Technology, project reference: UIDB/04561/2020.
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Khalili Golmankhaneh, A., Welch, K., Serpa, C. et al. Non-standard analysis for fractal calculus. J Anal 31, 1895–1916 (2023). https://doi.org/10.1007/s41478-022-00543-6
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DOI: https://doi.org/10.1007/s41478-022-00543-6