On Fractional Geometry of Curves
Open Access
- 9 October 2021
- journal article
- research article
- Published by MDPI AG in Fractal and Fractional
- Vol. 5 (4) , 161
Abstract
Fractional Differential Geometry of curves is discussed, with the help of a new fractional derivative, the Λ-fractional derivative, with the corresponding Λ-fractional space. Λ-Fractional derivative completely conforms with the demands of Differential Topology, for the existence of a differential. Therefore Fractional Differential Geometry is established in that Λ-space. The results are pulled back to the initial space.Keywords
This publication has 30 references indexed in Scilit:
- Advanced Topics in Fractional DynamicsAdvances in Mathematical Physics, 2013
- A Fractional Model of Continuum MechanicsJournal of Elasticity, 2011
- A fractional calculus approach to nonlocal elasticityThe European Physical Journal Special Topics, 2011
- Peridynamic Theory of Solid Mechanics2010
- Non-local continuum mechanics and fractional calculusMechanics Research Communications, 2006
- Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further resultsComputers & Mathematics with Applications, 2006
- On the connection between the order of fractional calculus and the dimensions of a fractal functionChaos, Solitons & Fractals, 2005
- Mechanics with fractional derivativesPhysical Review E, 1997
- Nonconservative Lagrangian and Hamiltonian mechanicsPhysical Review E, 1996
- Definition of Physically Consistent Damping Laws with Fractional DerivativesZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1995