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.
Описание: This Volume Contains Pedagogical, Review And Research Level Papers On Fractional Stochastic And Quantum Processes Which Have Been The Focus Of Intensive Mathematical, Experimental, And Computational Studies Due To Their Widening Spectrum Of Applications In Natural And Social Sciences. Novel Vis--Vis Standard Approaches In Fractional Stochastic Analysis Are Presented Together With Experimental And Theoretical Highlights In Applications To Single Particle Tracking, Organic Semiconductors, Polymer Structure, Complex Systems, And Finance, Among Others.
Описание: Unlike other fractional programming related titles, this book offers a "direct" approach to LFP and to duality in LFP, which is new in many aspects. First, the original LFP problem is considered as it is, without reducing it to an LP problem. Moreover, LFP is considered to be a generalization of LP and so most of the results are formulated in such a way that appropriate results of LP may be obtained as a special case of LFP. On the other hand, this approach makes it possible to compare dual variables in LP and LFP and to describe the relationship between them. In this respect, important (and new) application possibilities of duality appear in different parts of the book. The book provides readers with the basic knowledge necessary to build LFP models, to solve LFP problems and to utilize the optimal solution obtained. Moreover, the book contains detailed information on WinGULF, a software package developed by the author especially for linear-fractional programming. The package is designed to solve LFP problems with continuous as well as integer variables. The special "Student Edition" version of the package is free of charge and may be downloaded from the author's web page.
Описание: A secret traveller to the Tibetan capital of Lhasa, the author was forced to live, dress and behave as a Tibetan in order to remain undetected. Because of his unique perspective, he was able to provide an excellent description of the diplomatic, political, military and industrial situation of the country in the 1920s. Provides developments on fractional differential and fractional integro-differential equations involving many different potentially useful operators of fractional calculus. This book is application oriented and it contains the theory of Fractional Differential Equations. It provides problems and directions for further investigations.
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.
Описание: Fractional processes are widely found in science, technology and engineering systems. In Fractional Processes and Fractional-order Signal Processing, some complex random signals, characterized by the presence of a heavy-tailed distribution or non-negligible dependence between distant observations (local and long memory), are introduced and examined from the ‘fractional’ perspective using simulation, fractional-order modeling and filtering and realization of fractional-order systems. These fractional-order signal processing (FOSP) techniques are based on fractional calculus, the fractional Fourier transform and fractional lower-order moments. Fractional Processes and Fractional-order Signal Processing: presents fractional processes of fixed, variable and distributed order studied as the output of fractional-order differential systems; introduces FOSP techniques and the fractional signals and fractional systems point of view; details real-world-application examples of FOSP techniques to demonstrate their utility; and provides important background material on Mittag–Leffler functions, the use of numerical inverse Laplace transform algorithms and supporting MATLAB® codes together with a helpful survey of relevant webpages. Readers will be able to use the techniques presented to re-examine their signals and signal-processing methods. This text offers an extended toolbox for complex signals from diverse fields in science and engineering. It will give academic researchers and practitioners a novel insight into the complex random signals characterized by fractional properties, and some powerful tools to analyze those signals.
Описание: Offers an overview of the author`s work on the fields of fractional calculus and waves in linear viscoelastic media, which includes his contributions on the applications of special functions of the Mittag-Leffler and Wright types. This title is intended to serve as a general introduction to the above-mentioned areas of mathematical modeling.
Автор: Herrmann Richard Название: Fractional Calculus ISBN: 9814551074 ISBN-13(EAN): 9789814551076 Издательство: World Scientific Publishing Рейтинг: Цена: 19885 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.
Описание: Fractional Brownian motion (fBm) has been widely used to model a number of phenomena in diverse fields from biology to finance. This book presents an account of different definitions of stochastic integration for fBm, and to give applications of the resulting theory. It is suitable for students of mathematics, biology, and meteorology.
Автор: Yong Zhou Название: Fractional Evolution Equations and Inclusions ISBN: 012804277X ISBN-13(EAN): 9780128042779 Издательство: Elsevier Science Рейтинг: Цена: 10685 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Fractional evolution inclusions are an important form of differential inclusions within nonlinear mathematical analysis. They are generalizations of the much more widely developed fractional evolution equations (such as time-fractional diffusion equations) seen through the lens of multivariate analysis. Compared to fractional evolution equations, research on the theory of fractional differential inclusions is however only in its initial stage of development. This is important because differential models with the fractional derivative providing an excellent instrument for the description of memory and hereditary properties, and have recently been proved valuable tools in the modeling of many physical phenomena. The fractional order models of real systems are always more adequate than the classical integer order models, since the description of some systems is more accurate when the fractional derivative is used. The advantages of fractional derivatization become evident in modeling mechanical and electrical properties of real materials, description of rheological properties of rocks and in various other fields. Such models are interesting for engineers and physicists as well as so-called pure mathematicians. Phenomena investigated in hybrid systems with dry friction, processes of controlled heat transfer, obstacle problems and others can be described with the help of various differential inclusions, both linear and nonlinear. Fractional Evolution Equations and Inclusions is devoted to a rapidly developing area of the research for fractional evolution equations & inclusions and their applications to control theory. It studies Cauchy problems for fractional evolution equations, and fractional evolution inclusions with Hille-Yosida operators. It discusses control problems for systems governed by fractional evolution equations. Finally it provides an investigation of fractional stochastic evolution inclusions in Hilbert spa
Описание: The discovery of the Fractional Fourier Transform and its role in optics and data management provides a mathematical framework within which to discuss diffraction and other fundamental aspects of optical systems. This book explains how this transform has allowed the generalization of the Fourier transform and the notion of the frequency transform.
Автор: Das Название: Fractional Order Signal Processing ISBN: 3642231160 ISBN-13(EAN): 9783642231162 Издательство: Springer Рейтинг: Цена: 9713 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The book tries to briefly introduce the diverse literatures in the field of fractional order signal processing which is becoming an emerging topic among an interdisciplinary community of researchers. This book is aimed at postgraduate and beginning level research scholars who would like to work in the field of Fractional Order Signal processing (FOSP). The readers should have preliminary knowledge about basic signal processing techniques. Prerequisite knowledge of fractional calculus is not essential and is exposited at relevant places in connection to the appropriate signal processing topics. Basic signal processing techniques like filtering, estimation, system identification, etc. in the light of fractional order calculus are presented along with relevant application areas. The readers can easily extend these concepts to varied disciplines like image or speech processing, pattern recognition, time series forecasting, financial data analysis and modeling, traffic modeling in communication channels, optics, biomedical signal processing, electrochemical applications and many more. Adequate references are provided in each category so that the researchers can delve deeper into each area and broaden their horizon of understanding. Available MATLAB tools to simulate FOSP theories are also introduced so that the readers can apply the theoretical concepts right-away and gain practical insight in the specific domain.
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