Non-standard analysis for fractal calculus

The Journal of Analysis - Tập 31 - Trang 1895-1916 - 2023
Alireza Khalili Golmankhaneh1, Kerri Welch2, Cristina Serpa3,4, Palle E. T. Jørgensen5
1Department of Physics, Urmia Branch, Islamic Azad University, Urmia, Iran
2Faculty at California Institute of Integral Studies, San Francisco, USA
3ISEL, Instituto Superior de Engenharia, Lisboa, Portugal
4CMAFcIO, Faculdade de Ciências, Universidade de Lisboa, Lisboa, Portugal
5Department of Mathematics, The University of Iowa, Iowa, USA

Tóm tắt

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.

Tài liệu tham khảo

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