On the Darboux vector of a new fractional frame

Fractional derivatives are useful tools for many applications in different branch of science such as optics and engineering. In this paper, the ∧-fractional frame that is obtained along a space curve by using the ∧-fractional derivative is being examined in Euclidean E3 space. In addition, the Darboux vector of the ∧-fractional Frenet frame is constructed. Then the curvatures of the standard Frenet frame, the ∧-fractional Frenet frame and the ∧-fractional Darboux vector are compared geometrically.

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Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).