Fractional Calculus for Skeptics I. The Fractal Paradigm

Cover
Half Title
Series Page
Title Page
Copyright Page
Dedication
Contents
Preface
Author Bios
Nomenclature
CHAPTER 1: We Know That How?
	1.1. BRIEF HISTORY
	1.2. TECH-EVOLUTION PATTERNS
	1.3. LANGUAGE OF SET
	BIBLIOGRAPHY
CHAPTER 2: Complex ⇒ Nonsimple
	2.1. NEWTON’S WAY OF THINKING
	2.2. FRACTIONAL DISSIPATION
	2.3. THE INFINITESIMAL
	BIBLIOGRAPHY
CHAPTER 3: Nonsimple ⇔ FOT
	3.1. WHAT MANDELBROT SAW
	3.2. SCALING THEORY
	3.3. THE GAME HAS CHANGED
	BIBLIOGRAPHY
CHAPTER 4: FOO for Skeptics
	4.1. OPERATOR INTERPRETATION OF FOD
	4.2. RATE EQUATIONS
	4.3. FRACTIONAL-ORDER RATE EQUATIONS
	BIBLIOGRAPHY
CHAPTER 5: FOU for Skeptics
	5.1. PHYSICS-BASED STATISTICS
	5.2. INVERSE POWER LAWS (IPLS)
	5.3. NONSIMPLICITY HYPOTHESIS
	BIBLIOGRAPHY
CHAPTER 6: FOT for One, Two, Many
	6.1. “ONE VARIABLE”
	6.2. “TWO VARIABLES”
	6.3. “MANY VARIABLES”
	BIBLIOGRAPHY
APPENDIX A: Fractional-Order Operators
	A.1. RL− DERIVATIVE
	A.2. FRACTIONAL-ORDER STOCHASTIC EQUATION & SUBORDINATION
	A.3. FRACTIONAL BROWNIAN MOTION
	A.4. DECISION-MAKING MODEL (DMM)
	A.5. FRACTIONAL-ORDER KINETIC EQUATION
	BIBLIOGRAPHY
Index