Theory Of Fractional Evolution Equations PDF Download
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Author | : Yong Zhou |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 342 |
Release | : 2022-03-21 |
Genre | : Mathematics |
ISBN | : 3110769271 |
Download Theory of Fractional Evolution Equations Book in PDF, ePub and Kindle
Fractional evolution equations provide a unifying framework to investigate wellposedness of complex systems with fractional order derivatives. This monograph presents the existence, attractivity, stability, periodic solutions and control theory for time fractional evolution equations. The book contains an up-to-date and comprehensive stuff on the topic.
Author | : Yong Zhou |
Publisher | : World Scientific |
Total Pages | : 380 |
Release | : 2016-10-20 |
Genre | : Mathematics |
ISBN | : 9813148187 |
Download Basic Theory Of Fractional Differential Equations (Second Edition) Book in PDF, ePub and Kindle
This invaluable monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary and partial differential equations. It provides the readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, the technique of Picard operators, critical point theory and semigroup theory. Based on the research work carried out by the authors and other experts during the past seven years, the contents are very recent and comprehensive.In this edition, two new topics have been added, that is, fractional impulsive differential equations, and fractional partial differential equations including fractional Navier-Stokes equations and fractional diffusion equations.
Author | : Yong Zhou |
Publisher | : World Scientific |
Total Pages | : 516 |
Release | : 2023-10-06 |
Genre | : Mathematics |
ISBN | : 9811271704 |
Download Basic Theory Of Fractional Differential Equations (Third Edition) Book in PDF, ePub and Kindle
This accessible monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary differential equations and evolution equations. It is self-contained and unified in presentation, and provides the readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, Picard operators technique, critical point theory and semigroups theory. This book is based on the research work done so far by the author and other experts, and contains comprehensive up-to-date materials on the topic.In this third edition, four new topics have been added: Hilfer fractional evolution equations and infinite interval problems, oscillations and nonoscillations, fractional Hamiltonian systems, fractional Rayleigh-Stokes equations, and wave equations. The bibliography has also been updated and expanded.This book is useful to researchers, graduate or PhD students dealing with fractional calculus and applied analysis, differential equations, and related areas of research.
Author | : Yong Zhou |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 255 |
Release | : 2022-03-21 |
Genre | : Technology & Engineering |
ISBN | : 3110769360 |
Download Theory of Fractional Evolution Equations Book in PDF, ePub and Kindle
Fractional evolution equations provide a unifying framework to investigate wellposedness of complex systems with fractional order derivatives. This monograph presents the existence, attractivity, stability, periodic solutions and control theory for time fractional evolution equations. The book contains an up-to-date and comprehensive stuff on the topic.
Author | : Yong Zhou |
Publisher | : Academic Press |
Total Pages | : 296 |
Release | : 2016-02-05 |
Genre | : Mathematics |
ISBN | : 0128047755 |
Download Fractional Evolution Equations and Inclusions Book in PDF, ePub and Kindle
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 spaces. Systematic analysis of existence theory and topological structure of solution sets for fractional evolution inclusions and control systems Differential models with fractional derivative provide an excellent instrument for the description of memory and hereditary properties, and their description and working will provide valuable insights into the modelling of many physical phenomena suitable for engineers and physicists The book provides the necessary background material required to go further into the subject and explore the rich research literature
Author | : M.M. Djrbashian |
Publisher | : Birkhäuser |
Total Pages | : 266 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 3034885490 |
Download Harmonic Analysis and Boundary Value Problems in the Complex Domain Book in PDF, ePub and Kindle
As is well known, the first decades of this century were a period of elaboration of new methods in complex analysis. This elaboration had, in particular, one char acteristic feature, consisting in the interfusion of some concepts and methods of harmonic and complex analyses. That interfusion turned out to have great advan tages and gave rise to a vast number of significant results, of which we want to mention especially the classical results on the theory of Fourier series in L2 ( -7r, 7r) and their continual analog - Plancherel's theorem on the Fourier transform in L2 ( -00, +00). We want to note also two important Wiener and Paley theorems on parametric integral representations of a subclass of entire functions of expo nential type in the Hardy space H2 over a half-plane. Being under the strong influence of these results, the author began in the fifties a series of investigations in the theory of integral representations of analytic and entire functions as well as in the theory of harmonic analysis in the com plex domain. These investigations were based on the remarkable properties of the asymptotics of the entire function (p, J1 > 0), which was introduced into mathematical analysis by Mittag-Leffler for the case J1 = 1. In the process of investigation, the scope of some classical results was essentially enlarged, and the results themselves were evaluated.
Author | : Anatoly Kochubei |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 528 |
Release | : 2019-02-19 |
Genre | : Mathematics |
ISBN | : 3110571668 |
Download Fractional Differential Equations Book in PDF, ePub and Kindle
This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.
Author | : Wilfried Grecksch |
Publisher | : De Gruyter Akademie Forschung |
Total Pages | : 188 |
Release | : 1995 |
Genre | : Mathematics |
ISBN | : |
Download Stochastic Evolution Equations Book in PDF, ePub and Kindle
The authors give a self-contained exposition of the theory of stochastic evolution equations. Elements of infinite dimensional analysis, martingale theory in Hilbert spaces, stochastic integrals, stochastic convolutions are applied. Existence and uniqueness theorems for stochastic evolution equations in Hilbert spaces in the sense of the semigroup theory, the theory of evolution operators, and monotonous operators in rigged Hilbert spaces are discussed. Relationships between the different concepts are demonstrated. The results are used to concrete stochastic partial differential equations like parabolic and hyperbolic Ito equations and random constitutive equations of elastic viscoplastic materials. Furthermore, stochastic evolution equations in rigged Hilbert spaces are approximated by time discretization methods.
Author | : Igor Podlubny |
Publisher | : Elsevier |
Total Pages | : 366 |
Release | : 1998-10-27 |
Genre | : Mathematics |
ISBN | : 0080531989 |
Download Fractional Differential Equations Book in PDF, ePub and Kindle
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
Author | : Kaïs Ammari |
Publisher | : Cambridge University Press |
Total Pages | : 205 |
Release | : 2018 |
Genre | : Mathematics |
ISBN | : 1108412300 |
Download Evolution Equations Book in PDF, ePub and Kindle
The proceedings of a summer school held in 2015 whose theme was long time behavior and control of evolution equations.