Fractional dynamics
Fractional dynamics is a field of study in physics, mechanics, mathematics, and economics investigating the behavior of objects and systems that are described by using integrations and differentiation of fractional orders, by methods in the fractional calculus.
Derivatives and integrals of fractional orders are used to describe objects that can be characterized by power-law nonlocality, power-law long-term memory or fractal properties. Related applications include acoustical wave equations (see also the Applications section in the Fractional calculus article).
Further reading
- R. Metzler, J. Klafter, The random walk's guide to anomalous diffusion: A fractional dynamics approach. [1] Phys. Rep. Vol. 339 No.1. (2000) 1–77.
- B.J. West, M. Bologna, P. Grigolini, Physics of Fractal Operators. [2] Springer, 2003. 354 pages/ Chapter 3.
- G.M. Zaslavsky. Hamiltonian Chaos and Fractional Dynamics [3] Oxford University Press, 2008. 432 pages
- V. Lakshmikantham, S. Leela, J. Vasundhara Devi, Theory of Fractional Dynamic Systems [4] Cambridge Scientific Publishers, 2009.
- F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models[5] Imperial College Press, 2010.
- V.E. Tarasov, Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media [6] Springer, 2010. 504 pages
- R. Caponetto, G. Dongola, L. Fortuna, I. Petras, Fractional Order Systems: Modeling and Control Applications[7] World Scientific Publishing Company, 2010.
- A.C.J. Luo, V. Afraimovich (Eds.), Long-range Interaction, Stochasticity and Fractional Dynamics[8] Springer, 2010.
- J. Klafter, S.C. Lim, R. Metzler (Eds.), Fractional Dynamics. Recent Advances. (World Scientific, Singapore, 2011).
- T.M. Michelitsch, B. Collet, A.F. Nowakowski, F.C.G.A. Nicolleau, Fractional Laplacian matrix on the finite periodic linear chain and its periodic Riesz fractional derivative continuum limit J. Phys. A: Math. Theor. 48 (2015) 295202. [9]
- Changpin Li, Yujiang Wu, Ruisong Ye (Eds.), Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis: Fractional Dynamics, Network Dynamics, Classical Dynamics and Fractal Dynamics with Their Numerical Simulations[10] World Scientific, 2013.
- Fractional Differential Equations[11]
See also
- Fractional calculus
- Differintegral
- Acoustic attenuation
- Fractional quantum mechanics
- Fractional Schrödinger equation
References
- ↑ The random walk's guide to anomalous diffusion: A fractional dynamics approach.
- ↑ Physics of Fractal Operators.
- ↑ Hamiltonian Chaos and Fractional Dynamics.
- ↑ Theory of Fractional Dynamic Systems.
- ↑ Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models.
- ↑ Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media.
- ↑ Fractional Order Systems: Modeling and Control Applications.
- ↑ Long-range Interaction, Stochasticity and Fractional Dynamics.
- ↑ J. Phys. A: Math. Theor. 48 (2015) 295202. [dx.doi.org/doi:10.1088/1751-8113/48/29/295202]
- ↑ Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis: Fractional Dynamics, Network Dynamics, Classical Dynamics and Fractal Dynamics with Their Numerical Simulations
- ↑ Fractional Differential Equations (FDE)
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