Produktbild: Fuzzy Arbitrary Order System

Fuzzy Arbitrary Order System Fuzzy Fractional Differential Equations and Applications

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

16.08.2016

Verlag

John Wiley & Sons Inc

Seitenzahl

272

Maße (L/B/H)

23.6/15.7/2.3 cm

Gewicht

567 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-119-00411-0

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

16.08.2016

Verlag

John Wiley & Sons Inc

Seitenzahl

272

Maße (L/B/H)

23.6/15.7/2.3 cm

Gewicht

567 g

Auflage

1. Auflage

Sprache

Englisch

ISBN

978-1-119-00411-0

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: GPSR Kontakt

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  • Produktbild: Fuzzy Arbitrary Order System
  • PREFACE ix

    ACKNOWLEDGMENTS xiii

    1 Preliminaries of Fuzzy Set Theory 1

    Bibliography 7

    2 Basics of Fractional and Fuzzy Fractional Differential Equations 9

    Bibliography 12

    3 Analytical Methods for Fuzzy Fractional Differential Equations (FFDES) 15

    3.1 n-Term Linear Fuzzy Fractional Linear Differential Equations 16

    3.2 Proposed Methods 18

    Bibliography 28

    4 Numerical Methods for Fuzzy Fractional Differential Equations 31

    4.1 Homotopy Perturbation Method (HPM) 31

    4.2 Adomian Decomposition Method (ADM) 35

    4.3 Variational Iteration Method (VIM) 37

    Bibliography 39

    5 Fuzzy Fractional Heat Equations 41

    5.1 Arbitrary-Order Heat Equation 41

    5.2 Solution of Fuzzy Arbitrary-Order Heat Equations by HPM 41

    5.3 Numerical Examples 43

    5.4 Numerical Results 45

    Bibliography 47

    6 Fuzzy Fractional Biomathematical Applications 49

    6.1 Fuzzy Arbitrary-Order Predator-Prey Equations 49

    6.1.1 Particular Case 51

    6.2 Numerical Results of Fuzzy Arbitrary-Order Predator-Prey Equations 54

    Bibliography 65

    7 Fuzzy Fractional Chemical Problems 67

    7.1 Arbitrary-Order Rossler's Systems 67

    7.2 HPM Solution of Uncertain Arbitrary-Order Rossler's System 68

    7.3 Particular Case 71

    7.3.1 Special Case 73

    7.4 Numerical Results 78

    Bibliography 83

    8 Fuzzy Fractional Structural Problems 87

    8.1 Fuzzy Fractionally Damped Discrete System 88

    8.2 Uncertain Response Analysis 90

    8.2.1 Uncertain Step Function Response 90

    8.2.2 Uncertain Impulse Function Response 93

    8.3 Numerical Results 96

    8.3.1 Case Studies for Uncertain Step Function Response 97

    8.3.2 Case Studies for Uncertain Impulse Function Response 100

    8.4 Fuzzy Fractionally Damped Continuous System 101

    8.5 Uncertain Response Analysis 110

    8.5.1 Unit step Function Response 110

    8.5.2 Unit Impulse Function Response 111

    8.6 Numerical Results 112

    8.6.1 Case Studies for Fuzzy Unit Step Response 114

    8.6.2 Case Studies for Fuzzy Unit Impulse Response 115

    Bibliography 118

    9 Fuzzy Fractional Diffusion Problems 121

    9.1 Fuzzy Fractional-Order Diffusion Equation 121

    9.1.1 Double-Parametric-Based Solution of Uncertain

    Fractional-Order Diffusion Equation 123

    9.1.2 Solution Bounds for Different External Forces 125

    9.2 Numerical Results of Fuzzy Fractional Diffusion Equation 130

    Bibliography 139

    10 Uncertain Fractional Fornberg-Whitham Equations 141

    10.1 Parametric-Based Interval Fractional Fornberg-Whitham

    Equation 141

    10.2 Solution by VIM 143

    10.3 Solution Bounds for Different Interval Initial Conditions 145

    10.4 Numerical Results 148

    Bibliography 152

    11 Fuzzy Fractional Vibration Equation of Large Membrane 155

    11.1 Double-Parametric-Based Solution of Uncertain Vibration Equation of Large Membrane 156

    11.2 Solutions of Fuzzy Vibration Equation of Large Membrane 158

    11.3 Case Studies (Solution Bounds for Particular Cases) 160

    11.4 Numerical Results for Fuzzy Fractional Vibration Equation for Large Membrane 172

    Bibliography 188

    12 Fuzzy Fractional Telegraph Equations 191

    12.1 Double-Parametric-Based Fuzzy Fractional Telegraph Equations 191

    12.2 Solutions of Fuzzy Telegraph Equations Using Homotopy Perturbation Method 194

    12.3 Solution Bounds for Particular Cases 195

    12.4 Numerical Results for Fuzzy Fractional Telegraph Equations 199

    Bibliography 205

    13 Fuzzy Fokker-Planck Equation with Space and Time Fractional Derivatives 207

    13.1 Fuzzy Fractional Fokker-Planck Equation with Space and Time Fractional Derivatives 207

    13.2 Double-Parametric-Based Solution of Uncertain Fractional Fokker-Planck Equation 209

    13.2.1 Solution by HPM 209

    13.2.2 Solution By ADM 210

    13.3 Case Studies Using HPM and ADM 211

    13.3.1 Using HPM 211

    13.3.2 Using ADM 215

    13.4 Numerical Results of Fuzzy Fractional Fokker-Planck Equation 218

    Bibliography 220

    14 Fuzzy Fractional Bagley-Torvik Equations 223

    14.1 Various Types of Fuzzy Fractional Bagley-Torvik Equations 223

    14.2 Results and Discussions 231

    Bibliography 241

    APPENDIX A 243

    A.1 Fractionally Damped Spring-Mass System (Problem 1) 243

    A.1.1 Response Analysis 246

    A.1.2 Analytical Solution Using Fractional Green's Function 247

    A.2 Fractionally Damped Beam (Problem 2) 248

    A.2.1 Response Analysis 250

    A.2.2 Numerical Results 251

    Bibliography 255

    INDEX 257