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Non-standard analysis for fractal calculus

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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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Funding

Cristina Serpa acknowledges partial funding by national funds through FCT-Foundation for Science and Technology, project reference: UIDB/04561/2020.

Author information

Author notes

  1. Kerri Welch, Cristina Serpa and Palle E. T. Jørgensen contributed equally to this work.

Authors and Affiliations

  1. Department of Physics, Urmia Branch, Islamic Azad University, Urmia, 63896, Iran

    Alireza Khalili Golmankhaneh

  2. Faculty at California Institute of Integral Studies, San Francisco, CA, USA

    Kerri Welch

  3. ISEL, Instituto Superior de Engenharia, Lisboa, Portugal

    Cristina Serpa

  4. CMAFcIO, Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal

    Cristina Serpa

  5. Department of Mathematics, The University of Iowa, Iowa, 52242-1419, IA, USA

    Palle E. T. Jørgensen

Authors
  1. Alireza Khalili Golmankhaneh
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  2. Kerri Welch
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  3. Cristina Serpa
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  4. Palle E. T. Jørgensen
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Correspondence to Alireza Khalili Golmankhaneh.

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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

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