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Throughout this contribution, the concepts of regular curves, Frenet curves, arc length, Frenet frame and Frenet curvatures are generalized with the Caputo fractional derivative. A Frenet-Serret theorem is deduced from these concepts and a fractional fundamental theorem of the local theory of curves is proved.

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A Fundamental Theorem of Curves in the Euclidean Space with Caputo Fractional Derivatives

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  • 发表日期：

    2025年

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  • Roberto Carlos Balcázar-Araiza,
  • José Matías Navarro-Soza

摘要

Throughout this contribution, the concepts of regular curves, Frenet curves, arc length, Frenet frame and Frenet curvatures are generalized with the Caputo fractional derivative. A Frenet-Serret theorem is deduced from these concepts and a fractional fundamental theorem of the local theory of curves is proved.