Fractional trajectories: Decorrelation versus friction

A. Svenkeson, M.T. Beig, M. Turalska, B.J. West and P. Grigolini

Physica A: Statistical Mechanics and its Applications, 2013, vol. 392, issue 22, 5663-5672

Abstract: The fundamental connection between fractional calculus and subordination processes is explored and affords a physical interpretation of a fractional trajectory, that being an average over an ensemble of stochastic trajectories. Heretofore what has been interpreted as intrinsic friction, a form of non-Markovian dissipation that automatically arises from adopting the fractional calculus, is shown to be a manifestation of decorrelations between trajectories. We apply the general theory developed herein to the Lotka–Volterra ecological model, providing new insight into the final equilibrium state. The relaxation time to achieve this state is also considered.

Keywords: Fractional calculus; Subordination; Mittag-Leffler; Nonlinear operator; Decorrelation; Relaxation to equilibrium (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:392:y:2013:i:22:p:5663-5672

DOI: 10.1016/j.physa.2013.07.028

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