BookDOI
Fractional dynamics : recent advances
TLDR
In this article, the authors present a mathematical model of fractional dynamics of open quantum systems and apply it to fractional fractional diffusion processes in the context of Levy Flights.Abstract:
Ageing and Weak Ergodicity Breaking (E Barkai) Subdiffusion Reaction Processes (I Sokolov) Mathematics of Fractional Diffusion (R Gorenflo & F Mainardi) Fractional Dynamics of Open Quantum Systems (V E Tarasov) Fractional Quantum Field and Casimir Efffect (S C Lim & L P Teo) Aspects of Levy Flights: Confinement and Escape (A Chechkin) Fractional Material Derivative and Conditional CTRW (M Meerschaert) Subordination and Random Walks (A Weron & M Magdziarz) Bifractional Diffusion Processes (B Dybiec & E Gudowska) Plasma Physics and Fractional Diffusion (D Del Castillo-Negrete) Time Dependent Fields in Subdiffusion (I Goychuk & P Haenggi) Langevin Formulation of Fractional Fokker-Planck Equations (R Friedrich) Trapping and Subdiffusion (K Lindenberg) Fractional Langevin Equations (E Lutz) Fractional Diffusion Advection (B Baeumer) Fractional Dynamics and Financial Markets (E Scalas) Principles of Fractional Quantum Mechanics (N Laskin) Fractional Quantum Dynamics on Comb (A Iomin).read more
Citations
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Journal ArticleDOI
No violation of the Leibniz rule. No fractional derivative
TL;DR: It is proved that all fractional derivatives D α, which satisfy the Leibniz rule D α ( fg ) = ( D α f ) g + f ( D β g ) , should have the integer order α = 1.
Journal ArticleDOI
Existence of solutions for nonlinear fractional stochastic differential equations
TL;DR: In this paper, the existence of mild solutions for a class of fractional stochastic differential equations with impulses in Hilbert spaces was studied and sufficient conditions for mild solutions were formulated and proved.
Journal ArticleDOI
Conservation laws for time-fractional subdiffusion and diffusion-wave equations
TL;DR: In this article, a new technique for constructing conservation laws for fractional differential equations not having a Lagrangian is proposed based on the methods of Lie group analysis and employs the concept of nonlinear self-adjointness which is enhanced to the certain class of fractional evolution equations.
Journal ArticleDOI
Universal algorithm for identification of fractional Brownian motion. A case of telomere subdiffusion.
Krzysztof Burnecki,Eldad Kepten,Joanna Janczura,Irena Bronshtein,Yuval Garini,Aleksander Weron +5 more
TL;DR: A systematic statistical analysis of the recently measured individual trajectories of fluorescently labeled telomeres in the nucleus of living human cells establishes a rigorous mathematical characterization of the stochastic process and identifies the basic mathematical mechanisms behind the telomere motion.
Journal ArticleDOI
Review of Some Promising Fractional Physical Models
TL;DR: Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law nonlocality, powerlaw long-term memory or fractal properties by using integrations and differentiation of noninteger orders.