Applications of fractional calculus in equiaffine geometry: plane curves with fractional order
Muhittin Evren Aydın, Adela Mihai, Asıf Yokuş
Abstract
In this paper, we introduce the notions of equiaffine arclength and curvature with fractional order for a plane curve and compare them with the standard ones. By using these definitions, we obtain an equiaffine Frenet formula and then construct an analogue of the fundamental theorem. The plane curves of constant equiaffine curvature with fractional order are classified. Several examples are also illustrated.
Topics & Concepts
MathematicsPlane curveFrenet–Serret formulasCurvatureFractional calculusConstant curvaturePlane (geometry)Order (exchange)Differential geometry of curvesTorsion of a curveConstant (computer programming)GeometryTotal curvatureMathematical analysisMean curvatureCalculus (dental)Center of curvatureMean curvature flowDifferential equationEconomicsDifferential algebraic equationFinanceMedicineComputer scienceProgramming languageDentistryOrdinary differential equationFractional Differential Equations SolutionsAdvanced Differential Geometry ResearchIterative Methods for Nonlinear Equations