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Fuzzy arbitrary order system : fuzzy fractional differential equations and applications

Author: Snehashish Chakraverty; Smita Tapaswini; D Behera
Publisher: Hoboken, New Jersey : Wiley, [2016]
Edition/Format:   Print book : EnglishView all editions and formats
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Additional Physical Format: Online version:
Chakraverty, Snehashish.
Fuzzy arbitrary order system
Hoboken, New Jersey : John Wiley and Sons, Inc., [2016]
(DLC) 2016015086
Document Type: Book
All Authors / Contributors: Snehashish Chakraverty; Smita Tapaswini; D Behera
ISBN: 9781119004110 111900411X
OCLC Number: 907658214
Description: xiv, 258 pages : illustrations ; 25 cm
Contents: 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
Responsibility: Snehashish Chakraverty, Department of Mathematics, National Institute of Technology Rourkela, Odisha, India, Smita Tapaswini, College of Mathematics and Statistics, Chongqing University, Chongqing, P.R. China, Department of Mathematics KIIT University, Bhubaneswar, Odisha, India, Diptiranjan Behera, Institute of Reliability Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, P.R. China.

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