Fractional market dynamics

By Nick Laskin. 2000

433 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c2f577abc95aa8ed61d2523fc7eda75acd24b4fb

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In Economics and Econometrics

In Finance

In Statistical and Nonlinear Physics

Citations in the corpus

Chaos in the Newton–Leipnik system with fractional order (2008, background): “Recently, many systems have been identified that display fractional-order dynamics, such as viscoelastic systems [3–5], dielectric polarization [6], electrode–electrolyte polarization [7], electromagnetic waves [8], quantitative finance [9], quantum evolution of complex system [10], and the control ”
A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations (2016, background): “example the behavior of many systems, such as physical phenomena having memory and genetic characteristics, can be adequately modeled by fractional differential systems (see, for example, [9], [29]).”
An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov–Petrovskii–Piskunov Equation (2019, background): “In economics, it is known that some finance systems can display fractional order dynamics [18].”
Concentration phenomenon for fractional nonlinear Schr\"{o}dinger equations (2013, background): “Recently, Laskin extended the fractality concept and formulated fractional quantum mechanics as a path integral over the Lévy flights paths [50, 49, 52, 51].”
Existence and uniqueness results for Cauchy problem of variable-order fractional differential equations (2013, background): “recent four decades, such as advection diffusion process [4], random walk [5], viscoelastic models [6], finance models [7], quantum evolution of complex systems [8], chemical reaction [9], biological models [10], and so forth.”
Stability analysis for nonlinear fractional-order systems based on comparison principle (2014, background): “In the past 20 years, more and more researchers have been becoming interested in the fractional calculus, because of the fact that many physical mechanisms in real world [1–12], can be elegantly described with the help of fractional calculus and fractional-order differential equations.”