Автор: Baleanu Dumitru Et Al Название: Fractional Calculus: Models And Numerical Methods ISBN: 9814355208 ISBN-13(EAN): 9789814355209 Издательство: World Scientific Publishing Цена: 18216.00 р. Наличие на складе: Есть у поставщикаПоставка под заказ. Описание: The subject of fractional calculus and its applications (that is, convolution-type pseudo-differential operators including integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, mainly due to its applications in diverse fields of science and engineering. These operators have been used to model problems with anomalous dynamics, however, they also are an effective tool as filters and controllers, and they can be applied to write complicated functions in terms of fractional integrals or derivatives of elementary functions, and so on.This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models.All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book was written with a trade-off in mind between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. Numerical code is also provided.
This book aims to introduce some new trends and results on the study of the fractional differential equations, and to provide a good understanding of this field to beginners who are interested in this field, which is the authors' beautiful hope.
This book describes theoretical and numerical aspects of the fractional partial differential equations, including the authors' researches in this field, such as the fractional Nonlinear SchrOdinger equations, fractional Landau-Lifshitz equations and fractional Ginzburg-Landau equations. It also covers enough fundamental knowledge on the fractional derivatives and fractional integrals, and enough background of the fractional PDEs.
Описание: Classical trigonometry plays a very important role relative to integer order calculus, and together with the common exponential function, provides solutions for linear differential equations.
Автор: Almeida Ricardo, Pooseh Shakoor, Torres Delfim F. Название: Computational Methods in the Fractional Calculus of Variations ISBN: 1783266406 ISBN-13(EAN): 9781783266401 Издательство: World Scientific Publishing Рейтинг: Цена: 10296.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book fills a gap in the literature by introducing numerical techniques to solve problems of the Fractional Calculus of Variations (FCV). In most cases, finding the analytic solution to such problems is extremely difficult or even impossible, and numerical methods need to be used.
Автор: Herrmann Richard Название: Fractional Calculus ISBN: 9814551074 ISBN-13(EAN): 9789814551076 Издательство: World Scientific Publishing Рейтинг: Цена: 25344.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Latest Edition: Fractional Calculus: An Introduction for Physicists (3rd Edition)The book presents a concise introduction to the basic methods and strategies in fractional calculus and enables the reader to catch up with the state of the art in this field as well as to participate and contribute in the development of this exciting research area.The contents are devoted to the application of fractional calculus to physical problems. The fractional concept is applied to subjects in classical mechanics, group theory, quantum mechanics, nuclear physics, hadron spectroscopy and quantum field theory and it will surprise the reader with new intriguing insights.This new, extended edition now also covers additional chapters about image processing, folded potentials in cluster physics, infrared spectroscopy and local aspects of fractional calculus. A new feature is exercises with elaborated solutions, which significantly supports a deeper understanding of general aspects of the theory. As a result, this book should also be useful as a supporting medium for teachers and courses devoted to this subject.
Автор: Fallahgoul, Hassan Название: Fractional Calculus and Fractional Processes with Applications to ISBN: 0128042486 ISBN-13(EAN): 9780128042489 Издательство: Elsevier Science Рейтинг: Цена: 9264.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Fractional Calculus and Fractional Processes with Applications to Financial Economics presents the theory and application of fractional calculus and fractional processes to financial data. Fractional calculus dates back to 1695 when Gottfried Wilhelm Leibniz first suggested the possibility of fractional derivatives. Research on fractional calculus started in full earnest in the second half of the twentieth century. The fractional paradigm applies not only to calculus, but also to stochastic processes, used in many applications in financial economics such as modelling volatility, interest rates, and modelling high-frequency data. The key features of fractional processes that make them interesting are long-range memory, path-dependence, non-Markovian properties, self-similarity, fractal paths, and anomalous diffusion behaviour. In this book, the authors discuss how fractional calculus and fractional processes are used in financial modelling and finance economic theory. It provides a practical guide that can be useful for students, researchers, and quantitative asset and risk managers interested in applying fractional calculus and fractional processes to asset pricing, financial time-series analysis, stochastic volatility modelling, and portfolio optimization.
Автор: Namsrai Khavtgai Название: Universal Formulas In Integral And Fractional Differential Calculus ISBN: 9814675598 ISBN-13(EAN): 9789814675598 Издательство: World Scientific Publishing Рейтинг: Цена: 15048.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This table-top reference book presents unique and traditional analytic calculations, and features more than a hundred universal formulas where one can calculate by hand enormous numbers of definite integrals, fractional derivatives and inverse operators.
Автор: Torres Delfim F. M. Название: Introduction to the Fractional Calculus of Variations ISBN: 1848169663 ISBN-13(EAN): 9781848169661 Издательство: World Scientific Publishing Рейтинг: Цена: 10454.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Suitable for graduate students and ambitious undergraduates in mathematics and mechanics, this title offers an introduction to the subject of Fractional Calculus of Variations (FCV). It describes non-conservative systems in mechanics.
Автор: Molica Bisci Название: Variational Methods for Nonlocal Fractional Problems ISBN: 1107111943 ISBN-13(EAN): 9781107111943 Издательство: Cambridge Academ Рейтинг: Цена: 21226.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Devoted to the variational analysis of problems described by nonlocal operators, this book will appeal to a wide range of researchers and graduate students in mathematics, especially those interested in nonlinear phenomena. A careful balance is struck between rigorous mathematics and physical applications.
Автор: Podlubny, Igor. Название: Fractional differential equations : ISBN: 0125588402 ISBN-13(EAN): 9780125588409 Издательство: Elsevier Science Рейтинг: Цена: 16505.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Intended for readers who are new to the fields of fractional derivatives and fractional-order mathematical models, this covers the topics necessary for initial study and immediate application of fractional derivatives fractional differential equations. It also includes tables of fractional derivatives.
Автор: Xiao Jun Yang Название: Local Fractional Integral Transforms and Their Applications ISBN: 0128040025 ISBN-13(EAN): 9780128040027 Издательство: Elsevier Science Рейтинг: Цена: 11620.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors. The methods of integral transforms via local fractional calculus have been used to solve various local fractional ordinary and local fractional partial differential equations and also to figure out the presence of the fractal phenomenon. The book presents the basics of the local fractional derivative operators and investigates some new results in the area of local integral transforms.
Provides applications of local fractional Fourier Series
Discusses definitions for local fractional Laplace transforms
Explains local fractional Laplace transforms coupled with analytical methods
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