Bengochea, G.; Ortigueira, M. Fractional Line Integral. Mathematics2021, 9, 1150.
Bengochea, G.; Ortigueira, M. Fractional Line Integral. Mathematics 2021, 9, 1150.
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
MATHEMATICS & COMPUTER SCIENCE, General Mathematics
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