دانلود کتاب Fractional Calculus for Skeptics I. The Fractal Paradigm

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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