Fractional Calculus and Dynamic Approach to Complexity Page: I
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Beig, Mirza Tanweer Ahmad. Fractional Calculus and Dynamic Approach to
Complexity. Doctor of Philosophy (Physics), December 2015, 101 pp., 13 figures,
references, 92 titles.
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.
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Beig, Mirza Tanweer Ahmad. Fractional Calculus and Dynamic Approach to Complexity, dissertation, December 2015; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc822832/m1/2/: accessed January 20, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .