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Fractional Differential Equations
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 reade...
Distributed-Order Dynamic Systems
Distributed-order differential equations, a generalization of fractional calculus, are of increasing importance in many fields of science and engineering from the behaviour of complex dielectric media to the modelling of nonlinear systems. This Brief will broaden the toolbox available to researchers interested in modeling, analysis, control and filtering. It contains contextual material outlining the progression from integer-order, through fractional-order to distributed-order systems. Stability issues are addressed with graphical and numerical results highlighting the fundamental differences between constant-, integer-, and distributed-order treatments. The power of the distributed-order mo...
Kindergarten of Fractional Calculus
This book presents a simplified deliberation of fractional calculus, which will appeal not only to beginners, but also to various applied science mathematicians and engineering researchers. The text develops the ideas behind this new field of mathematics, beginning at the most elementary level, before discussing its actual applications in different areas of science and engineering. This book shows that the simple, classical laws based on Newtonian calculus, which work quite well under limiting and idealized conditions, are not of much use in describing the dynamics of actual systems. As such, the application of non-Newtonian, or generalized, calculus in the governing equations, allows the order of differentiation and integration to take on non-integer values.
Functional Fractional Calculus for System Identification and Controls
In this book, not only are mathematical abstractions discussed in a lucid manner, but also several practical applications are given particularly for system identification, description and then efficient controls. The reader gets a feeling of the wide applicability of fractional calculus in the field of science and engineering. With this book, a starter can understand the concepts of this emerging field with a minimal effort and basic mathematics.
Distributed-Order Dynamic Systems
Distributed-order differential equations, a generalization of fractional calculus, are of increasing importance in many fields of science and engineering from the behaviour of complex dielectric media to the modelling of nonlinear systems. This Brief will broaden the toolbox available to researchers interested in modeling, analysis, control and filtering. It contains contextual material outlining the progression from integer-order, through fractional-order to distributed-order systems. Stability issues are addressed with graphical and numerical results highlighting the fundamental differences between constant-, integer-, and distributed-order treatments. The power of the distributed-order mo...
Fractal Analysis
Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Let us begin with the fractional calculus-fractal geometry relationship, which allows for modeling with extreme precision of phenomena such as diffusion in porous media with fractional partial differential equations in fractal objects. Where the order of the equation is the same as the fractal dimension, this allows us to make calculations with enormous precision in diffusion phenomena-particularly in the oil industry, for new spillage prevention. Main applications to industry, design of fractal antennas to receive all frequencies and that is used in all cell phones, spacecraft, radars, image processing, measure, porosity, turbulence, scattering theory. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book: "Part I: Petroleum Industry and Numerical Analysis"; "Part II: Fractal Antennas, Spacecraft, Radars, Image Processing, and Measure"; and "Part III: Scattering Theory, Porosity, and Turbulence." It's impossible to picture today's research without fractal analysis.
Fractional Calculus
Zusammenfassung: Fractional calculus and its applications are fascinating research areas in many engineering disciplines. This book is a comprehensive collection of research from the author's group, which is one of the most active in the fractional calculus community worldwide and is the birthplace of one of the four MATLAB toolboxes in fractional calculus, the FOTF Toolbox. The book presents high-precision solution algorithms for a variety of fractional-order differential equations, including nonlinear, delay, and boundary value equations. Currently, there are no other universal solvers available for the latter two types of equations. Through this book, readers can systematically study the mathematics and solution methods in the field of fractional calculus and apply these concepts to different engineering fields, particularly control systems engineering This book is a translation of an original Chinese edition. The translation of some chapters was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done
Challenging the Boundaries of Symbolic Computation
This volume consists of papers delivered at the International Mathematica Symposium 2003 OCo an interdisciplinary meeting bringing together users of Mathematica in research and education. It gathers research papers, reports on classroom practice, reports on the use of Mathematica in industry and commerce, and descriptions of fresh applications. List of contributors: J Nash, S Wolfram, R Maeder, B Buchberger and C McTague. Contents: Algebraic Computation; Applied Mathematics; Education; Physics; Pure Mathematics; Statistics and Probability; Visualisation; Miscellaneous. Readership: Users of Mathematica for research, education and industry; developers of Mathematica applications; users of symbolic computation methods."
Applications of Fractional Calculus to Modeling in Dynamics and Chaos
Applications of Fractional Calculus to Modeling in Dynamics and Chaos aims to present novel developments, trends, and applications of fractional-order derivatives with power law and Mittag-Leffler kernel in the areas of chemistry, mechanics, chaos, epidemiology, fluid mechanics, modeling, and engineering. Non-singular and non-local fractional-order derivatives have been applied in different chapters to describe complex problems. The book offers theory and practical applications for the solutions of real-life problems and will be of interest to graduate-level students, educators, researchers, and scientists interested in mathematical modeling and its diverse applications. Features Discusses real-world problems, theory, and applications Covers new developments and advances in the various areas of nonlinear dynamics, signal processing, and chaos Suitable to teach master’s and/or PhD-level graduate students, and can be used by researchers, from any field of the social, health, and physical sciences
Control Applications in Modern Power Systems
This book provides rigorous discussions, case studies, and recent developments in the emerging areas of a control system, especially load frequency control, wide-area monitoring, control and instrumentation, optimization, intelligent control, energy management system, SCADA systems, etc. The readers would be benefitted from enhancing their knowledge and skills in the domain areas. Also, this book may help the readers in developing new and innovative ideas. The book can be a valuable reference for researchers and professionals interested in developments in the control system.
