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Fuzzy Arbitrary Order System

Author: Snehashish Chakraverty
Publisher: John Wiley & Sons
ISBN: 111900411X
Size: 22.62 MB
Format: PDF, Kindle
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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: 1315355531
Size: 66.96 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.

Advances In Metaheuristics Algorithms Methods And Applications

Author: Erik Cuevas
Publisher: Springer
ISBN: 3319893092
Size: 31.12 MB
Format: PDF, ePub
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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.

New Trends In Nanotechnology And Fractional Calculus Applications

Author: Dumitru Baleanu
Publisher: Springer Science & Business Media
ISBN: 9789048132935
Size: 39.26 MB
Format: PDF
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In recent years fractional calculus has played an important role in various fields such as mechanics, electricity, chemistry, biology, economics, modeling, identification, control theory and signal processing. The scope of this book is to present the state of the art in the study of fractional systems and the application of fractional differentiation. Furthermore, the manufacture of nanowires is important for the design of nanosensors and the development of high-yield thin films is vital in procuring clean solar energy. This wide range of applications is of interest to engineers, physicists and mathematicians.

Random Ordinary Differential Equations And Their Numerical Solution

Author: Xiaoying Han
Publisher: Springer
ISBN: 981106265X
Size: 59.78 MB
Format: PDF, Docs
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This book is intended to make recent results on the derivation of higher order numerical schemes for random ordinary differential equations (RODEs) available to a broader readership, and to familiarize readers with RODEs themselves as well as the closely associated theory of random dynamical systems. In addition, it demonstrates how RODEs are being used in the biological sciences, where non-Gaussian and bounded noise are often more realistic than the Gaussian white noise in stochastic differential equations (SODEs). RODEs are used in many important applications and play a fundamental role in the theory of random dynamical systems. They can be analyzed pathwise with deterministic calculus, but require further treatment beyond that of classical ODE theory due to the lack of smoothness in their time variable. Although classical numerical schemes for ODEs can be used pathwise for RODEs, they rarely attain their traditional order since the solutions of RODEs do not have sufficient smoothness to have Taylor expansions in the usual sense. However, Taylor-like expansions can be derived for RODEs using an iterated application of the appropriate chain rule in integral form, and represent the starting point for the systematic derivation of consistent higher order numerical schemes for RODEs. The book is directed at a wide range of readers in applied and computational mathematics and related areas as well as readers who are interested in the applications of mathematical models involving random effects, in particular in the biological sciences.The level of this book is suitable for graduate students in applied mathematics and related areas, computational sciences and systems biology. A basic knowledge of ordinary differential equations and numerical analysis is required.

Issues In Logic Operations And Computational Mathematics And Geometry 2011 Edition

Author:
Publisher: ScholarlyEditions
ISBN: 1464964785
Size: 17.21 MB
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Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Logic, Operations, and Computational Mathematics and Geometry. The editors have built Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Logic, Operations, and Computational Mathematics and Geometry in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Intelligent Engineering Systems And Computational Cybernetics

Author: J.A. Tenreiro Machado
Publisher: Springer Science & Business Media
ISBN: 1402086784
Size: 62.61 MB
Format: PDF, Mobi
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Engineering practice often has to deal with complex systems of multiple variable and multiple parameter models almost always with strong non-linear coupling. The conventional analytical techniques-based approaches for describing and predicting the behaviour of such systems in many cases are doomed to failure from the outset, even in the phase of the construction of a more or less appropriate mathematical model. These approaches normally are too categorical in the sense that in the name of “modelling accuracy” they try to describe all the structural details of the real physical system to be modelled. This can significantly increase the intricacy of the model and may result in a enormous computational burden without achieving considerable improvement of the solution. The best paradigm exemplifying this situation may be the classic perturbation theory: the less significant the achievable correction, the more work has to be invested to obtain it. A further important component of machine intelligence is a kind of “structural uniformity” giving room and possibility to model arbitrary particular details a priori not specified and unknown. This idea is similar to the ready-to-wear industry, which introduced products, which can be slightly modified later on in contrast to tailor-made creations aiming at maximum accuracy from the beginning. These subsequent corrections can be carried out by machines automatically. This “learning ability” is a key element of machine intelligence. The past decade confirmed that the view of typical components of the present soft computing as fuzzy logic, neural computing, evolutionary computation and probabilistic reasoning are of complementary nature and that the best results can be applied by their combined application. Today, the two complementary branches of Machine Intelligence, that is, Artificial Intelligence and Computational Intelligence serve as the basis of Intelligent Engineering Systems. The huge number of scientific results published in Journal and conference proceedings worldwide substantiates this statement. The present book contains several articles taking different viewpoints in the field of intelligent systems.

Mathematical Methods In Engineering

Author: Nuno Miguel Fonseca Ferreira
Publisher: Springer
ISBN: 9400771835
Size: 42.53 MB
Format: PDF, ePub
View: 4742
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This book presents a careful selection of the contributions presented at the Mathematical Methods in Engineering (MME10) International Symposium, held at the Polytechnic Institute of Coimbra- Engineering Institute of Coimbra (IPC/ISEC), Portugal, October 21-24, 2010. The volume discusses recent developments about theoretical and applied mathematics toward the solution of engineering problems, thus covering a wide range of topics, such as: Automatic Control, Autonomous Systems, Computer Science, Dynamical Systems and Control, Electronics, Finance and Economics, Fluid Mechanics and Heat Transfer, Fractional Mathematics, Fractional Transforms and Their Applications, Fuzzy Sets and Systems, Image and Signal Analysis, Image Processing, Mechanics, Mechatronics, Motor Control and Human Movement Analysis, Nonlinear Dynamics, Partial Differential Equations, Robotics, Acoustics, Vibration and Control, and Wavelets.