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 of fractional calculus

Fractional calculus

Fractional calculus is a branch of mathematical analysis that studies the possibility of taking real number powers or complex number powers of the differentiation operator.and the integration operator J...

.

Derivatives and integrals of fractional orders are used to describe objects that can be characterized by power-law

Power law

A power law is a special kind of mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event , the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary...

 nonlocality

Nonlocality

In Classical physics, nonlocality is the direct influence of one object on another, distant object. In Quantum mechanics, nonlocality refers to the absence of a local, realist model in agreement with quantum mechanical predictions.Nonlocality may refer to:...

, power-law

Power law

A power law is a special kind of mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event , the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary...

 long-term memory or fractal

Fractal

A fractal has been defined as "a rough or fragmented geometric shape that can be split into parts, each of which is a reduced-size copy of the whole," a property called self-similarity...

 properties.

Further reading

• R. Caponetto, G. Dongola, L. Fortuna, I. Petras, Fractional Order Systems: Modeling and Control Applications World Scientific Publishing Company, 2010.
• V. Lakshmikantham, S. Leela, J. Vasundhara Devi, Theory of Fractional Dynamic Systems Cambridge Scientific Publishers, 2009.
• A.C.J. Luo, V. Afraimovich (Eds.), Long-range Interaction, Stochasticity and Fractional Dynamics Springer, 2010.
• F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models Imperial College Press, 2010.
• R. Metzler, J. Klafter, The random walk's guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep. Vol. 339 No.1. (2000) 1–77.
• V.E. Tarasov, Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media Springer, 2010. 450 pages
• B.J. West, M. Bologna, P. Grigolini, Physics of Fractal Operators. Springer, 2003. 354 pages/ Chapter 3.
• G.M. Zaslavsky. Hamiltonian Chaos and Fractional Dynamics Oxford University Press, 2008. 432 pages
• Fractional Differential Equations

See also

• Fractional calculus
  Fractional calculus
  Fractional calculus is a branch of mathematical analysis that studies the possibility of taking real number powers or complex number powers of the differentiation operator.and the integration operator J...
  
  
• Differintegral
• Fractional quantum mechanics
  Fractional quantum mechanics
  In physics, fractional quantum mechanics is a generalization of standard quantum mechanics. The term fractional quantum mechanics was coined by Nick Laskin...
  
  
• Fractional Schrödinger equation
  Fractional Schrödinger equation
  The fractional Schrödinger equation is a fundamental equation of fractional quantum mechanics. It was discovered by Nick Laskin as a result of extending the Feynman path integral, from the Brownian-like to Lévy-like quantum mechanical paths. The term fractional Schrödinger equation was coined by...