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Fuzzy Arbitrary Order System

Author: Snehashish Chakraverty
Publisher: John Wiley & Sons
ISBN: 111900411X
Size: 42.91 MB
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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.

Fuzzy Differential Equations And Applications For Engineers And Scientists

Author: S. Chakraverty
Publisher: CRC Press
ISBN: 1482244764
Size: 23.81 MB
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Differential equations play a vital role in the modeling of physical and engineering problems, such as those in solid and fluid mechanics, viscoelasticity, biology, physics, and many other areas. In general, the parameters, variables and initial conditions within a model are considered as being defined exactly. In reality there may be only vague, imprecise or incomplete information about the variables and parameters available. This can result from errors in measurement, observation, or experimental data; application of different operating conditions; or maintenance induced errors. To overcome uncertainties or lack of precision, one can use a fuzzy environment in parameters, variables and initial conditions in place of exact (fixed) ones, by turning general differential equations into Fuzzy Differential Equations ("FDEs"). In real applications it can be complicated to obtain exact solution of fuzzy differential equations due to complexities in fuzzy arithmetic, creating the need for use of reliable and efficient numerical techniques in the solution of fuzzy differential equations. These include fuzzy ordinary and partial, fuzzy linear and nonlinear, and fuzzy arbitrary order differential equations. This unique work?provides a new direction for the reader in the use of basic concepts of fuzzy differential equations, solutions and its applications. It can serve as an essential reference work for students, scholars, practitioners, researchers and academicians in engineering and science who need to model uncertain physical problems.

Theory And Applications Of Fractional Differential Equations

Author: Anatoliĭ Aleksandrovich Kilbas
Publisher: Elsevier
ISBN: 9780444518323
Size: 58.30 MB
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This work aims to present, in a systematic manner, results including the existence and uniqueness of solutions for the Cauchy Type and Cauchy problems involving nonlinear ordinary fractional differential equations.

Mathematical Techniques Of Fractional Order Systems

Author: Ahmad Taher Azar
Publisher: Elsevier
ISBN: 012813593X
Size: 26.38 MB
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Mathematical Techniques of Fractional Order Systems illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order circuit theorems from different perspectives in design, analysis and realizations, nonlinear fractional-order circuits and systems, the fractional-order memristive circuits and systems in design, analysis, emulators, simulation and experimental results. It is primarily meant for researchers from academia and industry, and for those working in areas such as control engineering, electrical engineering, computer science and information technology. This book is ideal for researchers working in the area of both continuous-time and discrete-time dynamics and chaotic systems. Discusses multidisciplinary applications with new fundamentals, modeling, analysis, design, realization and experimental results Includes circuits and systems based on new nonlinear elements Covers most of the linear and nonlinear fractional-order theorems that will solve many scientific issues for researchers Closes the gap between theoretical approaches and real-world applications Provides MATLAB® and Simulink code for many applications in the book

Advances In Metaheuristics Algorithms Methods And Applications

Author: Erik Cuevas
Publisher: Springer
ISBN: 3319893092
Size: 76.54 MB
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This book explores new alternative metaheuristic developments that have proved to be effective in their application to several complex problems. Though most of the new metaheuristic algorithms considered offer promising results, they are nevertheless still in their infancy. To grow and attain their full potential, new metaheuristic methods must be applied in a great variety of problems and contexts, so that they not only perform well in their reported sets of optimization problems, but also in new complex formulations. The only way to accomplish this is to disseminate these methods in various technical areas as optimization tools. In general, once a scientist, engineer or practitioner recognizes a problem as a particular instance of a more generic class, he/she can select one of several metaheuristic algorithms that guarantee an expected optimization performance. Unfortunately, the set of options are concentrated on algorithms whose popularity and high proliferation outstrip those of the new developments. This structure is important, because the authors recognize this methodology as the best way to help researchers, lecturers, engineers and practitioners solve their own optimization problems.

Fractional Order Control Systems

Author: Dingyü Xue
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110497190
Size: 54.93 MB
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This book explains the essentials of fractional calculus and demonstrates its application in control system modeling, analysis and design. It presents original research to find high-precision solutions to fractional-order differentiations and differential equations. Numerical algorithms and their implementations are proposed to analyze multivariable fractional-order control systems. Through high-quality MATLAB programs, it provides engineers and applied mathematicians with theoretical and numerical tools to design control systems. Contents Introduction to fractional calculus and fractional-order control Mathematical prerequisites Definitions and computation algorithms of fractional-order derivatives and Integrals Solutions of linear fractional-order differential equations Approximation of fractional-order operators Modelling and analysis of multivariable fractional-order transfer function Matrices State space modelling and analysis of linear fractional-order Systems Numerical solutions of nonlinear fractional-order differential Equations Design of fractional-order PID controllers Frequency domain controller design for multivariable fractional-order Systems Inverse Laplace transforms involving fractional and irrational Operations FOTF Toolbox functions and models Benchmark problems for the assessment of fractional-order differential equation algorithms

Fractional Differential Equations

Author: Igor Podlubny
Publisher: Elsevier
ISBN: 9780080531984
Size: 20.37 MB
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This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers, from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional' is used instead of the word 'arbitrary'. This book is written for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, and feel that they need them for developing more adequate mathematical models. In this book, not only applied scientists, but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research. A reader will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems, analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications. A unique survey of many applications of fractional calculus Presents basic theory Includes a unified presentation of selected classical results, which are important for applications Provides many examples Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives

Fuzzy Differential Equations In Various Approaches

Author: Luciana Takata Gomes
Publisher: Springer
ISBN: 3319225758
Size: 33.42 MB
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This book may be used as reference for graduate students interested in fuzzy differential equations and researchers working in fuzzy sets and systems, dynamical systems, uncertainty analysis, and applications of uncertain dynamical systems. Beginning with a historical overview and introduction to fundamental notions of fuzzy sets, including different possibilities of fuzzy differentiation and metric spaces, this book moves on to an overview of fuzzy calculus thorough exposition and comparison of different approaches. Innovative theories of fuzzy calculus and fuzzy differential equations using fuzzy bunches of functions are introduced and explored. Launching with a brief review of essential theories, this book investigates both well-known and novel approaches in this field; such as the Hukuhara differentiability and its generalizations as well as differential inclusions and Zadeh’s extension. Through a unique analysis, results of all these theories are examined and compared.

Recent Advances On Soft Computing And Data Mining

Author: Tutut Herawan
Publisher: Springer
ISBN: 3319076922
Size: 41.72 MB
Format: PDF, ePub, Mobi
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This book constitutes the refereed proceedings of the First International Conference on Soft Computing and Data Mining, SCDM 2014, held in Universiti Tun Hussein Onn Malaysia, in June 16th-18th, 2014. The 65 revised full papers presented in this book were carefully reviewed and selected from 145 submissions, and organized into two main topical sections; Data Mining and Soft Computing. The goal of this book is to provide both theoretical concepts and, especially, practical techniques on these exciting fields of soft computing and data mining, ready to be applied in real-world applications. The exchanges of views pertaining future research directions to be taken in this field and the resultant dissemination of the latest research findings makes this work of immense value to all those having an interest in the topics covered.