Work

A New Fractional Curvature of Curves and Surfaces in Euclidean Space Using the Caputo’s Fractional Derivative

Year: 2024

Type: article

Abstract: In this paper, the authors generalize the fractional curvature of plane curves introduced by Rubio et al. in 2023, to regular curves in the Euclidean space R3, and study the geometric properties of the curve using Caputo’s fractional derivative. Furthermore, we introduce a new definition of fractional curvature and fractional mean curvature of a regular surface, using fractional principal curvatures; and prove that such concepts are invariant under isometries; i.e., they belong to the intrinsic geometry of the regular surface. Also, a geometric interpretation is given to Caputo’s fractional derivative of algebraic polynomials.

Source: Symmetry

DOI: 10.3390/sym16101350

Authors: Franco Rubio-López, Obidio Rubio, Ronald León, Alexis Rodriguez, Daniel Chucchucan

Institutions: National University of Trujillo, Private University of the North

Language: English

Topic: Advanced Differential Geometry Research

Subfield: Astronomy and Astrophysics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

OpenAlex ID: W4403402534

FWCI: 0.382

Cites: 21

Cited by: 2

Related to: 10