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Fractional-time quantum dynamics [PDF]
Physical Review E, 2009 Application of the fractional calculus to quantum processes is presented. In particular, the quantum dynamics is considered in the framework of the fractional time Schrödinger equation (SE), which differs from the standard SE by the fractional time derivative: $\frac{\prt}{\prt t}\to \frac{\prt^α}{\prt t^α}$. It is shown that for $α=1/2$ the fractional
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FRACTIONAL DYNAMICS IN GENETIC ALGORITHMS [PDF]
IFAC Proceedings Volumes, 2006 Abstract This paper investigate the fractional-order dynamics during the evolution of a Genetic Algorithm (GA). In order to study the phenomena involved in the GA population evolution, the mutation is exposed to excitation perturbations during some generationsand the corresponding fitness variations are evaluated.
Pires, E. J. Solteiro +2 more
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Fractional dynamical model for the generation of ECG like signals from filtered coupled Van-der Pol oscillators [PDF]
, 2013 In this paper, an incommensurate fractional order (FO) model has been proposed to generate ECG like waveforms. Earlier investigation of ECG like waveform generation is based on two identical Van-der Pol (VdP) family of oscillators, which are coupled by ...
Das, Saptarshi, Maharatna, Koushik
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Generalized continuous-time random walks, subordination by hitting times, and fractional dynamics [PDF]
, 2009 Functional limit theorems for continuous-time random walks (CTRW) are found in the general case of dependent waiting times and jump sizes that are also position dependent.
Kolokoltsov, V. N. (Vasiliĭ Nikitich)
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, 2015 The book is devoted to recent developments in the theory of fractional calculus and its applications. Particular attention is paid to the applicability of this currently popular research field in various branches of pure and applied mathematics. In particular, the book focuses on the more recent results in mathematical physics, engineering applications,
Srivastava, Hari M. +2 more
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Anomalous Diffusion by the Fractional Fokker-Planck Equation and L\ue9vy Stable Processes [PDF]
, 2018 The work presented here is a review of current developments in modelling\ua0anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives\ua0and Langevin dynamics where L\ub4evy fluctuations are introduced to model the ...
Anderson, Johan +3 more
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Diffusive representations for fractional Laplacian: systems theory framework and numerical issues [PDF]
, 2009 Bridging the gap between an abstract definition of pseudo-differential operators, such as (-\Delta)^{\gamma} for - 1/2 < \gamma < 1/2, and a concrete way to represent them has proved difficult; deriving stable numerical schemes for such operators is not ...
Matignon, Denis
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Fractional random walk lattice dynamics [PDF]
, 2017 We analyze time-discrete and time-continuous 'fractional' random walks on undirected regular networks with special focus on cubic periodic lattices in n = 1, 2, 3,.. dimensions.
Riascos A.P. +4 more
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Fractional-time Schrödinger equation: Fractional dynamics on a comb [PDF]
Chaos, Solitons & Fractals, 2011 The physical relevance of the fractional time derivative in quantum mechanics is discussed. It is shown that the introduction of the fractional time Scrödinger equation (FTSE) in quantum mechanics by analogy with the fractional diffusion $\frac{\prt}{\prt t}\rightarrow \frac{\prt^α}{\prt t^α}$ can lead to an essential deficiency in the quantum ...
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Dynamics with low-level fractionality [PDF]
Physica A: Statistical Mechanics and its Applications, 2006 LaTeX, 24 pages, to be published in Physica ...
Tarasov, Vasily E., Zaslavsky, George M.
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