Fuzzy arbitrary order system : fuzzy fractional differential equations and applications / by Snehashish Chakraverty, Smita Tapaswini, D. Behera.
Presents a systematic treatment of fuzzy fractional differential equations as well as newly developed computational methods to model uncertain physical problems Complete with comprehensive results and solutions, Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications d...
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Full Text (via ProQuest) |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Hoboken, New Jersey :
John Wiley and Sons, Inc.,
[2016]
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| Series: | Online access with DDA: Askews (Maths)
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| Subjects: |
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| 100 | 1 | |a Chakraverty, Snehashish. | |
| 245 | 1 | 0 | |a Fuzzy arbitrary order system : |b fuzzy fractional differential equations and applications / |c by Snehashish Chakraverty, Smita Tapaswini, D. Behera. |
| 264 | 1 | |a Hoboken, New Jersey : |b John Wiley and Sons, Inc., |c [2016] | |
| 300 | |a 1 online resource | ||
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| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Print version record and CIP data provided by publisher. | |
| 520 | |a Presents a systematic treatment of fuzzy fractional differential equations as well as newly developed computational methods to model uncertain physical problems Complete with comprehensive results and solutions, Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications details newly developed methods of fuzzy computational techniquesneeded to model solve uncertainty. Fuzzy differential equations are solved via various analytical andnumerical methodologies, and this book presents their importance for problem solving, prototypeengineering design, and systems testing in uncertain environments. In recent years, modeling of differential equations for arbitrary and fractional order systems has been increasing in its applicability, and as such, the authors feature examples from a variety of disciplines to illustrate the practicality and importance of the methods within physics, applied mathematics, engineering, and chemistry, to name a few. The fundamentals of fractional differential equations and the basic preliminaries of fuzzy fractional differential equations are first introduced, followed by numerical solutions, comparisons of various methods, and simulated results. In addition, fuzzy ordinary, partial, linear, and nonlinear fractional differential equations are addressed to solve uncertainty in physical systems. In addition, this book features: - Basic preliminaries of fuzzy set theory, an introduction of fuzzy arbitrary order differential equations, and various analytical and numerical procedures for solving associated problems - Coverage on a variety of fuzzy fractional differential equations including structural, diffusion, and chemical problems as well as heat equations and biomathematical applications - Discussions on how to model physical problems in terms of nonprobabilistic methods and provides systematic coverage of fuzzy fractional differential equations and its applications - Uncertainties in systems and processes with a fuzzy concept Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications is an ideal resource for practitioners, researchers, and academicians in applied mathematics, physics, biology, engineering, computer science, and chemistry who need to model uncertain physical phenomena and problems. The book is appropriate for graduate-level courses on fractional differential equations for students majoring in applied mathematics, engineering, physics, and computer science. Snehashish Chakraverty, PhD, is Professor and Head of the Department of Mathematics at the National Institute of Technology, Rourkela in India. The author of five books and approximately 140 journal articles, his research interests include mathematical modeling, machine intelligence, uncertainty modeling, numerical analysis, and differential equations. Smita Tapaswini, PhD, is Assistant Professor in the Department of Mathematics at the Kalinga Institute of Industrial Technology University in India and is also Post-Doctoral Fellow at the College of Mathematics and Statistics at Chongqing University in China. Her research interests include fuzzy differential equations, fuzzy fractional differential equations, and numerical analysis. Diptiranjan Behera, PhD, is Post-Doctoral Fellow at the Institute of Reliability Engineering in the School of Mechatronics Engineering at the University of Electronic Science and Technology of China. His current research interests include interval and fuzzy mathematics, fuzzy finite element methods, and fuzzy structural analysis. | ||
| 505 | 0 | |a Cover; Title Page; Copyright; Contents; Preface; Acknowledgments; Chapter 1 Preliminaries of Fuzzy Set Theory; Bibliography; Chapter 2 Basics of Fractional and Fuzzy Fractional Differential Equations; Bibliography; Chapter 3 Analytical Methods for Fuzzy Fractional Differential Equations (FFDES); 3.1 n-Term Linear Fuzzy Fractional Linear Differential Equations; 3.2 Proposed Methods; Bibliography; Chapter 4 Numerical Methods for Fuzzy Fractional Differential Equations; 4.1 Homotopy Perturbation Method (HPM); 4.2 Adomian Decomposition Method (ADM); 4.3 Variational Iteration Method (VIM). | |
| 505 | 8 | |a 7.3.1 Special Case7.4 Numerical Results; Bibliography; Chapter 8 Fuzzy Fractional Structural Problems; 8.1 Fuzzy Fractionally Damped Discrete System; 8.2 Uncertain Response Analysis; 8.2.1 Uncertain Step Function Response; 8.2.2 Uncertain Impulse Function Response; 8.3 Numerical Results; 8.3.1 Case Studies for Uncertain Step Function Response; 8.3.2 Case Studies for Uncertain Impulse Function Response; 8.4 Fuzzy Fractionally Damped Continuous System; 8.5 Uncertain Response Analysis; 8.5.1 Unit step Function Response; 8.5.2 Unit Impulse Function Response; 8.6 Numerical Results. | |
| 505 | 8 | |a 8.6.1 Case Studies for Fuzzy Unit Step Response8.6.2 Case Studies for Fuzzy Unit Impulse Response; Bibliography; Chapter 9 Fuzzy Fractional Diffusion Problems; 9.1 Fuzzy Fractional-Order Diffusion Equation; 9.1.1 Double-Parametric-Based Solution of Uncertain Fractional-Order Diffusion Equation; 9.1.2 Solution Bounds for Different External Forces; 9.2 Numerical Results of Fuzzy Fractional Diffusion Equation; Bibliography; Chapter 10 Uncertain Fractional Fornberg-Whitham Equations; 10.1 Parametric-Based Interval Fractional Fornberg-Whitham Equation; 10.2 Solution by VIM. | |
| 505 | 8 | |a 10.3 Solution Bounds for Different Interval Initial Conditions10.4 Numerical Results; Bibliography; Chapter 11 Fuzzy Fractional Vibration Equation of Large Membrane; 11.1 Double-Parametric-Based Solution of Uncertain Vibration Equation of Large Membrane; 11.2 Solutions of Fuzzy Vibration Equation of Large Membrane; 11.3 Case Studies (Solution Bounds for Particular Cases); 11.4 Numerical Results for Fuzzy Fractional Vibration Equation for Large Membrane; Bibliography; Chapter 12 Fuzzy Fractional Telegraph Equations; 12.1 Double-Parametric-Based Fuzzy Fractional Telegraph Equations. | |
| 650 | 0 | |a Fractional differential equations. | |
| 650 | 0 | |a Fuzzy mathematics. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 7 | |a Differential equations |2 fast | |
| 650 | 7 | |a Fractional differential equations |2 fast | |
| 650 | 7 | |a Fuzzy mathematics |2 fast | |
| 700 | 1 | |a Tapaswini, Smita, |d 1987- | |
| 700 | 1 | |a Behera, D. |q (Diptiranjan), |d 1988- | |
| 776 | 0 | 8 | |i Print version: |a Chakraverty, Snehashish. |t Fuzzy arbitrary order system. |d Hoboken, New Jersey : John Wiley and Sons, Inc., [2016] |z 9781119004110 |w (DLC) 2016013567 |
| 830 | 0 | |a Online access with DDA: Askews (Maths) | |
| 856 | 4 | 0 | |u https://ebookcentral.proquest.com/lib/ucb/detail.action?docID=4635690 |z Full Text (via ProQuest) |
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| 952 | f | f | |p Can circulate |a University of Colorado Boulder |b Online |c Online |d Online |e QA314 |h Library of Congress classification |i web |