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Fractional Calculus and Dynamic Approach to Complexity

Fractional calculus enables the possibility of using real number powers or complex number powers of the differentiation operator. The fundamental connection between fractional calculus and subordination processes is explored and affords a physical interpretation for a fractional trajectory, that being an average over an ensemble of stochastic trajectories. With an ensemble average perspective, the explanation of the behavior of fractional chaotic systems changes dramatically. Before now what has been interpreted as intrinsic friction is actually a form of non-Markovian dissipation that automatically arises from adopting the fractional calculus, is shown to be a manifestation of decorrelations between trajectories. Nonlinear Langevin equation describes the mean field of a finite size complex network at criticality. Critical phenomena and temporal complexity are two very important issues of modern nonlinear dynamics and the link between them found by the author can significantly improve the understanding behavior of dynamical systems at criticality. The subject of temporal complexity addresses the challenging and especially helpful in addressing fundamental physical science issues beyond the limits of reductionism.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc822832
Date12 1900
CreatorsBeig, Mirza Tanweer Ahmad
ContributorsGrigolini, Paolo, Krokhin, Arkadii, Roberts, James Andrew, Rostovtsev, Yuri
PublisherUniversity of North Texas
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formatviii, 101 pages : illustrations (chiefly color), Text
RightsPublic, Beig, Mirza Tanweer Ahmad, Copyright, Copyright is held by the author, unless otherwise noted. All rights Reserved.

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