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Author : Smail Djebali
Publisher :
ISBN 13 :
Total Pages : 148 pages
Book Rating : 4.:/5 (79 download)
Download or read book Existence and Structure of Solution Sets for Impulsive Differential Inclusions written by Smail Djebali and published by . This book was released on 2012 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Smaïl Djebali
Publisher : Walter de Gruyter
ISBN 13 : 3110293560
Total Pages : 474 pages
Book Rating : 4.1/5 (12 download)
Download or read book Solution Sets for Differential Equations and Inclusions written by Smaïl Djebali and published by Walter de Gruyter. This book was released on 2012-12-06 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gives a systematic presentation of classical and recent results obtained in the last couple of years. It comprehensively describes the methods concerning the topological structure of fixed point sets and solution sets for differential equations and inclusions. Many of the basic techniques and results recently developed about this theory are presented, as well as the literature that is disseminated and scattered in several papers of pioneering researchers who developed the functional analytic framework of this field over the past few decades. Several examples of applications relating to initial and boundary value problems are discussed in detail. The book is intended to advanced graduate researchers and instructors active in research areas with interests in topological properties of fixed point mappings and applications; it also aims to provide students with the necessary understanding of the subject with no deep background material needed. This monograph fills the vacuum in the literature regarding the topological structure of fixed point sets and its applications.
Author : Mouffak Benchohra
Publisher : Hindawi Publishing Corporation
ISBN 13 : 977594550X
Total Pages : 381 pages
Book Rating : 4.7/5 (759 download)
Download or read book Impulsive Differential Equations and Inclusions written by Mouffak Benchohra and published by Hindawi Publishing Corporation. This book was released on 2006 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : John R. Graef
Publisher : Walter de Gruyter
ISBN 13 : 3110295318
Total Pages : 412 pages
Book Rating : 4.1/5 (12 download)
Download or read book Impulsive Differential Inclusions written by John R. Graef and published by Walter de Gruyter. This book was released on 2013-07-31 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations with impulses arise as models of many evolving processes that are subject to abrupt changes, such as shocks, harvesting, and natural disasters. These phenomena involve short-term perturbations from continuous and smooth dynamics, whose duration is negligible in comparison with the duration of an entire evolution. In models involving such perturbations, it is natural to assume these perturbations act instantaneously or in the form of impulses. As a consequence, impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, and so forth. There are also many different studies in biology and medicine for which impulsive differential equations provide good models. During the last 10 years, the authors have been responsible for extensive contributions to the literature on impulsive differential inclusions via fixed point methods. This book is motivated by that research as the authors endeavor to bring under one cover much of those results along with results by other researchers either affecting or affected by the authors' work. The questions of existence and stability of solutions for different classes of initial value problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems. In addition, since differential equations can be viewed as special cases of differential inclusions, significant attention is also given to relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simpler beginnings as well.
Author : Yong Zhou
Publisher : Springer
ISBN 13 : 9811066566
Total Pages : 278 pages
Book Rating : 4.8/5 (11 download)
Download or read book Topological Structure of the Solution Set for Evolution Inclusions written by Yong Zhou and published by Springer. This book was released on 2017-10-31 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book systematically presents the topological structure of solution sets and attractability for nonlinear evolution inclusions, together with its relevant applications in control problems and partial differential equations. It provides readers the background material needed to delve deeper into the subject and explore the rich research literature. In addition, the book addresses many of the basic techniques and results recently developed in connection with this theory, including the structure of solution sets for evolution inclusions with m-dissipative operators; quasi-autonomous and non-autonomous evolution inclusions and control systems; evolution inclusions with the Hille-Yosida operator; functional evolution inclusions; impulsive evolution inclusions; and stochastic evolution inclusions. Several applications of evolution inclusions and control systems are also discussed in detail. Based on extensive research work conducted by the authors and other experts over the past four years, the information presented is cutting-edge and comprehensive. As such, the book fills an important gap in the body of literature on the structure of evolution inclusions and its applications.
Author : Nikolai A. Perestyuk
Publisher : Walter de Gruyter
ISBN 13 : 3110218178
Total Pages : 325 pages
Book Rating : 4.1/5 (12 download)
Download or read book Differential Equations with Impulse Effects written by Nikolai A. Perestyuk and published by Walter de Gruyter. This book was released on 2011-07-27 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significant interest in the investigation of systems with discontinuous trajectories is explained by the development of equipment in which significant role is played by impulsive control systems and impulsive computing systems. Impulsive systems are also encountered in numerous problems of natural sciences described by mathematical models with conditions reflecting the impulsive action of external forces with pulses whose duration can be neglected. Differential equations with set-valued right-hand side arise in the investigation of evolution processes in the case of measurement errors, inaccuracy or incompleteness of information, action of bounded perturbations, violation of unique solvability conditions, etc. Differential inclusions also allow one to describe the dynamics of controlled processes and are widely used in the theory of optimal control. This monograph is devoted to the investigation of impulsive differential equations with set-valued and discontinuous right-hand sides. It is intended for researchers, lecturers, postgraduate students, and students of higher schools specialized in the field of the theory of differential equations, the theory of optimal control, and their applications.
Author : Georgi V. Smirnov
Publisher : American Mathematical Society
ISBN 13 : 1470468549
Total Pages : 226 pages
Book Rating : 4.4/5 (74 download)
Download or read book Introduction to the Theory of Differential Inclusions written by Georgi V. Smirnov and published by American Mathematical Society. This book was released on 2022-02-22 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: A differential inclusion is a relation of the form $dot x in F(x)$, where $F$ is a set-valued map associating any point $x in R^n$ with a set $F(x) subset R^n$. As such, the notion of a differential inclusion generalizes the notion of an ordinary differential equation of the form $dot x = f(x)$. Therefore, all problems usually studied in the theory of ordinary differential equations (existence and continuation of solutions, dependence on initial conditions and parameters, etc.) can be studied for differential inclusions as well. Since a differential inclusion usually has many solutions starting at a given point, new types of problems arise, such as investigation of topological properties of the set of solutions, selection of solutions with given properties, and many others. Differential inclusions play an important role as a tool in the study of various dynamical processes described by equations with a discontinuous or multivalued right-hand side, occurring, in particular, in the study of dynamics of economical, social, and biological macrosystems. They also are very useful in proving existence theorems in control theory. This text provides an introductory treatment to the theory of differential inclusions. The reader is only required to know ordinary differential equations, theory of functions, and functional analysis on the elementary level. Chapter 1 contains a brief introduction to convex analysis. Chapter 2 considers set-valued maps. Chapter 3 is devoted to the Mordukhovich version of nonsmooth analysis. Chapter 4 contains the main existence theorems and gives an idea of the approximation techniques used throughout the text. Chapter 5 is devoted to the viability problem, i.e., the problem of selection of a solution to a differential inclusion that is contained in a given set. Chapter 6 considers the controllability problem. Chapter 7 discusses extremal problems for differential inclusions. Chapter 8 presents stability theory, and Chapter 9 deals with the stabilization problem.
Author : Anatoli? Mikha?lovich Samo?lenko
Publisher : World Scientific
ISBN 13 : 9789810224165
Total Pages : 482 pages
Book Rating : 4.2/5 (241 download)
Download or read book Impulsive Differential Equations written by Anatoli? Mikha?lovich Samo?lenko and published by World Scientific. This book was released on 1995 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: For researchers in nonlinear science, this work includes coverage of linear systems, stability of solutions, periodic and almost periodic impulsive systems, integral sets of impulsive systems, optimal control in impulsive systems, and more.
Author : Gani T. Stamov
Publisher : Springer Science & Business Media
ISBN 13 : 3642275451
Total Pages : 235 pages
Book Rating : 4.6/5 (422 download)
Download or read book Almost Periodic Solutions of Impulsive Differential Equations written by Gani T. Stamov and published by Springer Science & Business Media. This book was released on 2012-03-09 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present book a systematic exposition of the results related to almost periodic solutions of impulsive differential equations is given and the potential for their application is illustrated.
Author : Sotiris K. Ntouyas
Publisher : MDPI
ISBN 13 : 3039432184
Total Pages : 518 pages
Book Rating : 4.0/5 (394 download)
Download or read book Fractional Differential Equations, Inclusions and Inequalities with Applications written by Sotiris K. Ntouyas and published by MDPI. This book was released on 2020-11-09 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last decade, there has been an increased interest in fractional differential equations, inclusions, and inequalities, as they play a fundamental role in the modeling of numerous phenomena, in particular, in physics, biomathematics, blood flow phenomena, ecology, environmental issues, viscoelasticity, aerodynamics, electrodynamics of complex medium, electrical circuits, electron-analytical chemistry, control theory, etc. This book presents collective works published in the recent Special Issue (SI) entitled "Fractional Differential Equation, Inclusions and Inequalities with Applications" of the journal Mathematics. This Special Issue presents recent developments in the theory of fractional differential equations and inequalities. Topics include but are not limited to the existence and uniqueness results for boundary value problems for different types of fractional differential equations, a variety of fractional inequalities, impulsive fractional differential equations, and applications in sciences and engineering.
Author : Yong Zhou
Publisher : World Scientific
ISBN 13 : 9813148187
Total Pages : 380 pages
Book Rating : 4.8/5 (131 download)
Download or read book Basic Theory Of Fractional Differential Equations (Second Edition) written by Yong Zhou and published by World Scientific. This book was released on 2016-10-20 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Marat Akhmet
Publisher : Springer
ISBN 13 : 9811031800
Total Pages : 175 pages
Book Rating : 4.8/5 (11 download)
Download or read book Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities written by Marat Akhmet and published by Springer. This book was released on 2017-01-23 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types – those with jumps present either in the right-hand side, or in trajectories or in the arguments of solutions of equations. The results obtained can be applied to various fields, such as neural networks, brain dynamics, mechanical systems, weather phenomena and population dynamics. Developing bifurcation theory for various types of differential equations, the book is pioneering in the field. It presents the latest results and provides a practical guide to applying the theory to differential equations with various types of discontinuity. Moreover, it offers new ways to analyze nonautonomous bifurcation scenarios in these equations. As such, it shows undergraduate and graduate students how bifurcation theory can be developed not only for discrete and continuous systems, but also for those that combine these systems in very different ways. At the same time, it offers specialists several powerful instruments developed for the theory of discontinuous dynamical systems with variable moments of impact, differential equations with piecewise constant arguments of generalized type and Filippov systems.
Author :
Publisher : ScholarlyEditions
ISBN 13 : 1464964785
Total Pages : 1531 pages
Book Rating : 4.4/5 (649 download)
Download or read book Issues in Logic, Operations, and Computational Mathematics and Geometry: 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 1531 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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/.
Author : Saïd Abbas
Publisher : Elsevier
ISBN 13 : 044323602X
Total Pages : 400 pages
Book Rating : 4.4/5 (432 download)
Download or read book Fractional Difference, Differential Equations, and Inclusions written by Saïd Abbas and published by Elsevier. This book was released on 2024-01-16 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of fractional calculus (FC) is more than 300 years old, and it presumably stemmed from a question about a fractional-order derivative raised in communication between L'Hopital and Leibniz in the year 1695. This branch of mathematical analysis is regarded as the generalization of classical calculus, as it deals with the derivative and integral operators of fractional order. The tools of fractional calculus are found to be of great utility in improving the mathematical modeling of many natural phenomena and processes occurring in the areas of engineering, social, natural, and biomedical sciences. Fractional Difference, Differential Equations, and Inclusions: Analysis and Stability is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for several classes of functional fractional difference equations and inclusions. Some equations include delay effects of finite, infinite, or state-dependent nature. Others are subject to impulsive effect which may be fixed or non-instantaneous. The tools used to establish the existence results for the proposed problems include fixed point theorems, densifiability techniques, monotone iterative technique, notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. All the abstract results are illustrated by examples in applied mathematics, engineering, biomedical, and other applied sciences. Introduces notation, definitions, and foundational concepts of fractional q-calculus Presents existence and attractivity results for a class of implicit fractional q-difference equations in Banach and Fréchet spaces Focuses on the study of a class of coupled systems of Hilfer and Hilfer-Hadamard fractional differential equations
Author : Yong Zhou
Publisher : Academic Press
ISBN 13 : 0128047755
Total Pages : 296 pages
Book Rating : 4.1/5 (28 download)
Download or read book Fractional Evolution Equations and Inclusions written by Yong Zhou and published by Academic Press. This book was released on 2016-02-05 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Yong Zhou
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110769271
Total Pages : 342 pages
Book Rating : 4.1/5 (17 download)
Download or read book Theory of Fractional Evolution Equations written by Yong Zhou and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-03-21 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311139218X
Total Pages : 314 pages
Book Rating : 4.1/5 (113 download)
Download or read book Nonautonomous Fractional Evolution Equations written by Yong Zhou and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-07-01 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional evolution equations describe various complex and nonlocal systems with memory. This volume investigates fractional evolution equations, in infinite intervals. The book covers a range of topics, including the existence, uniqueness, attractivity, and applications to fractional diffusion equations and fractional Schrodinger equations. Researchers and graduate students in pure and applied mathematics will find this a useful reference.
