Fractional line integral

Gabriel Bengochea, Manuel Ortigueira

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This paper proposed a definition of the fractional line integral, generalising the concept of the fractional definite integral. The proposal replicated the properties of the classic definite integral, namely the fundamental theorem of integral calculus. It was based on the concept of the fractional anti-derivative used to generalise the Barrow formula. To define the fractional line integral, the Grünwald–Letnikov and Liouville directional derivatives were introduced and their properties described. The integral was defined for a piecewise linear path first and, from it, for any regular curve.

Original languageEnglish
Article number1150
Number of pages11
Issue number10
Publication statusPublished - 2 May 2021


  • Fractional integral
  • Fractional line integral
  • Grünwald–Letnikov fractional derivative
  • Liouville fractional derivative


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