Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and ApplicationsPresents 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:
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 |
257 | |