Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications

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John Wiley & Sons, Aug 29, 2016 - Mathematics - 272 pages

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.

 

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Contents

Preliminaries of Fuzzy Set Theory
1
Basics of Fractional and Fuzzy Fractional Differential Equations
9
Analytical Methods for Fuzzy Fractional Differential Equations
15
Numerical Methods for Fuzzy Fractional Differential Equations
31
Fuzzy Fractional Heat Equations
41
Fuzzy Fractional Biomathematical Applications
49
Fuzzy Fractional Chemical Problems
67
Fuzzy Fractional Structural Problems
87
Fuzzy Fractional Diffusion Problems
121
Uncertain Fractional FornbergWhitham Equations
141
Fuzzy Fractional Vibration Equation of Large Membrane
155
Fuzzy Fractional Telegraph Equations
191
Fuzzy FokkerPlanck Equation with Space and Time Fractional
207
Fuzzy Fractional BagleyTorvik Equations
223
APPENDIX A
243
INDEX
257

6
97

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About the author (2016)

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.

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