Fractional Calculus and Dynamic Approach to Complexity

Description

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 ... continued below

Physical Description

viii, 101 pages : illustrations (chiefly color)

Creation Information

Beig, Mirza Tanweer Ahmad December 2015.

Context

This dissertation is part of the collection entitled: UNT Theses and Dissertations and was provided by UNT Libraries to Digital Library, a digital repository hosted by the UNT Libraries. It has been viewed 86 times , with 5 in the last month . More information about this dissertation can be viewed below.

Who

People and organizations associated with either the creation of this dissertation or its content.

Publisher

Rights Holder

For guidance see Citations, Rights, Re-Use.

  • Beig, Mirza Tanweer Ahmad

Provided By

UNT Libraries

With locations on the Denton campus of the University of North Texas and one in Dallas, UNT Libraries serves the school and the community by providing access to physical and online collections; The Portal to Texas History and UNT Digital Libraries; academic research, and much, much more.

Contact Us

What

Descriptive information to help identify this dissertation. Follow the links below to find similar items on the Digital Library.

Degree Information

Description

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.

Physical Description

viii, 101 pages : illustrations (chiefly color)

Language

Collections

This dissertation is part of the following collection of related materials.

UNT Theses and Dissertations

Theses and dissertations represent a wealth of scholarly and artistic content created by masters and doctoral students in the degree-seeking process. Some ETDs in this collection are restricted to use by the UNT community.

What responsibilities do I have when using this dissertation?

When

Dates and time periods associated with this dissertation.

Creation Date

  • December 2015

Added to The UNT Digital Library

  • March 20, 2016, 10:34 a.m.

Description Last Updated

  • May 30, 2017, 8:11 a.m.

Usage Statistics

When was this dissertation last used?

Yesterday: 0
Past 30 days: 5
Total Uses: 86

Interact With This Dissertation

Here are some suggestions for what to do next.

Start Reading

Citations, Rights, Re-Use

Beig, Mirza Tanweer Ahmad. Fractional Calculus and Dynamic Approach to Complexity, dissertation, December 2015; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc822832/: accessed December 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .