Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Fractional Line Integral

Version 1 : Received: 30 March 2021 / Approved: 31 March 2021 / Online: 31 March 2021 (21:45:06 CEST)

A peer-reviewed article of this Preprint also exists.

Bengochea, G.; Ortigueira, M. Fractional Line Integral. Mathematics 2021, 9, 1150. Bengochea, G.; Ortigueira, M. Fractional Line Integral. Mathematics 2021, 9, 1150.

Journal reference: Mathematics 2021, 9, 1150
DOI: 10.3390/math9101150


This paper proposes a definition of fractional line integral, generalising the concept of fractional definite integral. The proposal replicates the properties of the classic definite integral, namely the fundamental theorem of integral calculus. It is based on the concept of fractional anti-derivative used to generalise the Barrow formula. To define the fractional line integrals the Gr\"unwald-Letnikov and Liouville directional derivatives are introduced and their properties described. The integral is defined first for broken line paths and afterwards to any regular curve


Fractional Integral; Grünwald-Letnikov Fractional Derivative; Fractional Line Integral; Liouville Fractional Derivative



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