1st Edition

Fractional Calculus View of Complexity
Tomorrow’s Science

ISBN 9781498738002
Published October 9, 2015 by CRC Press
303 Pages 12 Color & 26 B/W Illustrations

USD $115.00

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Book Description

This book is not a text devoted to a pedagogical presentation of a specialized topic nor is it a monograph focused on the author's area of research. It accomplishes both these things while providing a rationale for why the reader ought to be interested in learning about fractional calculus. This book is for researchers who has heard about many of these scientifically exotic activities, but could not see how they fit into their own scientific interests, or how they could be made compatible with the way they understand science. It is also for beginners who have not yet decided where their scientific talents could be most productively applied. The book provides insight into the long-term direction of science and show how to develop the skills necessary to successfully do research in the twenty-first century.

Table of Contents


The Challenge of Complexity

Little Science, Big Science


Chapter Overviews

After Thoughts

Yesterday's Science

Simple Linearity

Complicated Linearity

Nonlinear Dynamics

After Thoughts

Appendix Chapter 2

New Ways of Thinking

Why Now?

Through the Looking Glass

Non-differentiablity can be Physical

The size effect

After Thoughts

Simple Fractional Operators

Random Walks

Fractional Derivatives

Fractional Rate Equations

After Thoughts

Tomorrow’s Dynamics

What We Think We Know; Linear Systems



Fractional Linear System

Applications of FLE

Control of Complexity

Fractional Logistic Equation

Fractional Leibniz Rule

After Thoughts

Appendix Chapter 5

Fractional Cooperation

HRV and Lévy Statistics

Fractional Wave Equations


Fractional Magnetization Equations

Fractional Search Hypothesis

The Network Effect

After Thoughts

Strange Statistics

Fractional Hamiltonian Formalism

Anomalous Transport

Fractional Fokker-Planck Equation

Fractional Sturm-Liouville Theory

Fractional Kinetics Equation

Physiology and Complexity Loss

Diffusion Entropy

After Thoughts

Appendices Chapter 7

What have we learned?

Why the fractional calculus?

Conformation Bias and Scientific Truth

Final Thoughts

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