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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.
Abstract
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
Keywords
Fractional Integral; Grünwald-Letnikov Fractional Derivative; Fractional Line Integral; Liouville Fractional Derivative
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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