Fractional trajectories: Decorrelation versus friction |
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Authors: | A Svenkeson MT Beig M Turalska BJ West P Grigolini |
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Institution: | 1. Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, TX 76203-1427, USA;2. Department of Physics, Duke University, Durham, NC 27708, USA;3. Information Science Directorate, Army Research Office, Research Triangle Park, NC 27709, USA |
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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. |
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Keywords: | Fractional calculus Subordination Mittag-Leffler Nonlinear operator Decorrelation Relaxation to equilibrium |
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