Fractional Line Integral

Gabriel Bengochea and Manuel Ortigueira
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Gabriel Bengochea: Academia de Matemática, Universidad Autónoma de la Ciudad de México, Ciudad de México 09790, Mexico
Manuel Ortigueira: CTS-UNINOVA and DEE, NOVA School of Science and Technology, NOVA University of Lisbon, Quinta da Torre, 2829-516 Caparica, Portugal

Mathematics, 2021, vol. 9, issue 10, 1-11

Abstract: 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.

Keywords: fractional integral; Grünwald–Letnikov fractional derivative; fractional line integral; Liouville fractional derivative (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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