Advanced Functional Evolution Equations And Inclusions

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Advanced Functional Evolution Equations and Inclusions

Saïd Abbas,Mouffak Benchohra
Advanced Functional Evolution Equations and Inclusions Book PDF

Author : Saïd Abbas,Mouffak Benchohra
Publisher : Springer
Page : 408 pages
File Size : 42,5 Mb
Release : 2015-06-30
Category : Mathematics
ISBN : 9783319177687

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Advanced Functional Evolution Equations and Inclusions by Saïd Abbas,Mouffak Benchohra Pdf

This book presents up-to-date results on abstract evolution equations and differential inclusions in infinite dimensional spaces. It covers equations with time delay and with impulses, and complements the existing literature in functional differential equations and inclusions. The exposition is devoted to both local and global mild solutions for some classes of functional differential evolution equations and inclusions, and other densely and non-densely defined functional differential equations and inclusions in separable Banach spaces or in Fréchet spaces. The tools used include classical fixed points theorems and the measure-of non-compactness, and each chapter concludes with a section devoted to notes and bibliographical remarks. This monograph is particularly useful for researchers and graduate students studying pure and applied mathematics, engineering, biology and all other applied sciences.

Fractional Difference, Differential Equations, and Inclusions

Saïd Abbas,Bashir Ahmad,Mouffak Benchohra,Abdelkrim Salim
Fractional Difference Differential Equations and Inclusions Book PDF

Author : Saïd Abbas,Bashir Ahmad,Mouffak Benchohra,Abdelkrim Salim
Publisher : Elsevier
Page : 400 pages
File Size : 46,6 Mb
Release : 2024-01-16
Category : Computers
ISBN : 9780443236020

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Fractional Difference, Differential Equations, and Inclusions by Saïd Abbas,Bashir Ahmad,Mouffak Benchohra,Abdelkrim Salim Pdf

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

Fractional Evolution Equations and Inclusions

Yong Zhou
Fractional Evolution Equations and Inclusions Book PDF

Author : Yong Zhou
Publisher : Academic Press
Page : 294 pages
File Size : 47,6 Mb
Release : 2016-02-05
Category : Mathematics
ISBN : 9780128047750

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Fractional Evolution Equations and Inclusions by Yong Zhou Pdf

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

Topological Structure of the Solution Set for Evolution Inclusions

Yong Zhou,Rong-Nian Wang,Li Peng
Topological Structure of the Solution Set for Evolution Inclusions Book PDF

Author : Yong Zhou,Rong-Nian Wang,Li Peng
Publisher : Springer
Page : 269 pages
File Size : 47,6 Mb
Release : 2017-10-31
Category : Mathematics
ISBN : 9789811066566

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Topological Structure of the Solution Set for Evolution Inclusions by Yong Zhou,Rong-Nian Wang,Li Peng Pdf

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.

Theory of Fractional Evolution Equations

Yong Zhou,Bashir Ahmad,Ahmed Alsaedi
Theory of Fractional Evolution Equations Book PDF

Author : Yong Zhou,Bashir Ahmad,Ahmed Alsaedi
Publisher : Walter de Gruyter GmbH & Co KG
Page : 342 pages
File Size : 53,9 Mb
Release : 2022-03-21
Category : Mathematics
ISBN : 9783110769272

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Theory of Fractional Evolution Equations by Yong Zhou,Bashir Ahmad,Ahmed Alsaedi Pdf

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.

Advances in Differential and Difference Equations with Applications 2020

Dumitru Baleanu
Advances in Differential and Difference Equations with Applications 2020 Book PDF

Author : Dumitru Baleanu
Publisher : MDPI
Page : 348 pages
File Size : 54,5 Mb
Release : 2021-01-20
Category : Computers
ISBN : 9783039368709

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Advances in Differential and Difference Equations with Applications 2020 by Dumitru Baleanu Pdf

It is very well known that differential equations are related with the rise of physical science in the last several decades and they are used successfully for models of real-world problems in a variety of fields from several disciplines. Additionally, difference equations represent the discrete analogues of differential equations. These types of equations started to be used intensively during the last several years for their multiple applications, particularly in complex chaotic behavior. A certain class of differential and related difference equations is represented by their respective fractional forms, which have been utilized to better describe non-local phenomena appearing in all branches of science and engineering. The purpose of this book is to present some common results given by mathematicians together with physicists, engineers, as well as other scientists, for whom differential and difference equations are valuable research tools. The reported results can be used by researchers and academics working in both pure and applied differential equations.

Fractional Differential Equations And Inclusions: Classical And Advanced Topics

Said Abbas,Mouffak Benchohra,Jamal Eddine Lazreg,Juan J Nieto,Yong Zhou
Fractional Differential Equations And Inclusions Classical And Advanced Topics Book PDF

Author : Said Abbas,Mouffak Benchohra,Jamal Eddine Lazreg,Juan J Nieto,Yong Zhou
Publisher : World Scientific
Page : 326 pages
File Size : 47,9 Mb
Release : 2023-02-02
Category : Mathematics
ISBN : 9789811261275

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Fractional Differential Equations And Inclusions: Classical And Advanced Topics by Said Abbas,Mouffak Benchohra,Jamal Eddine Lazreg,Juan J Nieto,Yong Zhou Pdf

This monograph is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for various classes of functional differential equations or inclusions involving the Hadamard or Hilfer fractional derivative. Some equations present delay which may be finite, infinite, or state-dependent. Others are subject to impulsive effect which may be fixed or non-instantaneous.Readers will find the book self-contained and unified in presentation. It provides the necessary background material required to go further into the subject and explores the rich research literature in detail. Each chapter concludes with a section devoted to notes and bibliographical remarks and all abstract results are illustrated by examples. The tools used include many classical and modern nonlinear analysis methods such as fixed-point theorems, as well as some notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. It is useful for researchers and graduate students for research, seminars, and advanced graduate courses, in pure and applied mathematics, physics, mechanics, engineering, biology, and all other applied sciences.

New Trends in the Applications of Differential Equations in Sciences

Angela Slavova
New Trends in the Applications of Differential Equations in Sciences Book PDF

Author : Angela Slavova
Publisher : Springer Nature
Page : 457 pages
File Size : 54,8 Mb
Release : 2023-03-17
Category : Mathematics
ISBN : 9783031214844

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New Trends in the Applications of Differential Equations in Sciences by Angela Slavova Pdf

This book convenes peer-reviewed, selected papers presented at the Ninth International Conference New Trends in the Applications of Differential Equations in Sciences (NTADES) held in Sozopol, Bulgaria, June 17–20, 2022. The works are devoted to many applications of differential equations in different fields of science. A number of phenomena in nature (physics, chemistry, biology) and in society (economics) result in problems leading to the study of linear and nonlinear differential equations, stochastic equations, statistics, analysis, numerical analysis, optimization, and more. The main topics are presented in the five parts of the book - applications in mathematical physics, mathematical biology, financial mathematics, neuroscience, and fractional analysis. In this volume, the reader will find a wide range of problems concerning recent achievements in both theoretical and applied mathematics. The main goal is to promote the exchange of new ideas and research between scientists, who develop and study differential equations, and researchers, who apply them for solving real-life problems. The book promotes basic research in mathematics leading to new methods and techniques useful for applications of differential equations. The NTADES 2022 conference was organized in cooperation with the Society of Industrial and Applied Mathematics (SIAM), the major international organization for Industrial and Applied Mathematics and for the promotion of interdisciplinary collaboration between applied mathematics and science, engineering, finance, and neuroscience.

Existence Families, Functional Calculi and Evolution Equations

Ralph DeLaubenfels
Existence Families Functional Calculi and Evolution Equations Book PDF

Author : Ralph DeLaubenfels
Publisher : Springer
Page : 254 pages
File Size : 43,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540483229

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Existence Families, Functional Calculi and Evolution Equations by Ralph DeLaubenfels Pdf

This book presents an operator-theoretic approach to ill-posed evolution equations. It presents the basic theory, and the more surprising examples, of generalizations of strongly continuous semigroups known as 'existent families' and 'regularized semigroups'. These families of operators may be used either to produce all initial data for which a solution in the original space exists, or to construct a maximal subspace on which the problem is well-posed. Regularized semigroups are also used to construct functional, or operational, calculi for unbounded operators. The book takes an intuitive and constructive approach by emphasizing the interaction between functional calculus constructions and evolution equations. One thinks of a semigroup generated by A as etA and thinks of a regularized semigroup generated by A as etA g(A), producing solutions of the abstract Cauchy problem for initial data in the image of g(A). Material that is scattered throughout numerous papers is brought together and presented in a fresh, organized way, together with a great deal of new material.

Time-Dependent Subdifferential Evolution Inclusions and Optimal Control

Shouchuan Hu,Nikolaos Socrates Papageorgiou
Time Dependent Subdifferential Evolution Inclusions and Optimal Control Book PDF

Author : Shouchuan Hu,Nikolaos Socrates Papageorgiou
Publisher : American Mathematical Soc.
Page : 81 pages
File Size : 41,8 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821807798

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Time-Dependent Subdifferential Evolution Inclusions and Optimal Control by Shouchuan Hu,Nikolaos Socrates Papageorgiou Pdf

This volume studies multivalued evolution equations driven by time-dependent subdifferential operators and optimal control problems for such systems. The formulation is general enough to incorporate problems with time varying constraints. For evolution inclusions, existence relaxation and structural results for the solution set are proved. For optimal control problems, a general existence theory is developed, different forms of the relaxed problem are introduced and studied, well-posedness properties are investigated and the precise relation between the properties of relaxability and well-posedness is established. Various examples of systems which fit in the abstract framework are analyzed.

Implicit Fractional Differential and Integral Equations

Saïd Abbas,Mouffak Benchohra,John R. Graef,Johnny Henderson
Implicit Fractional Differential and Integral Equations Book PDF

Author : Saïd Abbas,Mouffak Benchohra,John R. Graef,Johnny Henderson
Publisher : Walter de Gruyter GmbH & Co KG
Page : 359 pages
File Size : 41,6 Mb
Release : 2018-02-05
Category : Mathematics
ISBN : 9783110553185

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Implicit Fractional Differential and Integral Equations by Saïd Abbas,Mouffak Benchohra,John R. Graef,Johnny Henderson Pdf

This book deals with the existence and stability of solutions to initial and boundary value problems for functional differential and integral equations and inclusions involving the Riemann-Liouville, Caputo, and Hadamard fractional derivatives and integrals. A wide variety of topics is covered in a mathematically rigorous manner making this work a valuable source of information for graduate students and researchers working with problems in fractional calculus. Contents Preliminary Background Nonlinear Implicit Fractional Differential Equations Impulsive Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Nonlinear Implicit Fractional Differential Equations Boundary Value Problems for Impulsive NIFDE Integrable Solutions for Implicit Fractional Differential Equations Partial Hadamard Fractional Integral Equations and Inclusions Stability Results for Partial Hadamard Fractional Integral Equations and Inclusions Hadamard–Stieltjes Fractional Integral Equations Ulam Stabilities for Random Hadamard Fractional Integral Equations

Functional Analytic Methods for Evolution Equations

Giuseppe Da Prato,Peer Christian Kunstmann,Irena Lasiecka,Alessandra Lunardi,Roland Schnaubelt,Lutz Weis
Functional Analytic Methods for Evolution Equations Book PDF

Author : Giuseppe Da Prato,Peer Christian Kunstmann,Irena Lasiecka,Alessandra Lunardi,Roland Schnaubelt,Lutz Weis
Publisher : Springer Science & Business Media
Page : 486 pages
File Size : 47,5 Mb
Release : 2004-09-22
Category : Mathematics
ISBN : 3540230300

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Functional Analytic Methods for Evolution Equations by Giuseppe Da Prato,Peer Christian Kunstmann,Irena Lasiecka,Alessandra Lunardi,Roland Schnaubelt,Lutz Weis Pdf

This book consists of five introductory contributions by leading mathematicians on the functional analytic treatment of evolutions equations. In particular the contributions deal with Markov semigroups, maximal L^p-regularity, optimal control problems for boundary and point control systems, parabolic moving boundary problems and parabolic nonautonomous evolution equations. The book is addressed to PhD students, young researchers and mathematicians doing research in one of the above topics.

Mechanics of Advanced Functional Materials

Biao Wang
Mechanics of Advanced Functional Materials Book PDF

Author : Biao Wang
Publisher : Springer Science & Business Media
Page : 537 pages
File Size : 50,6 Mb
Release : 2013-07-24
Category : Science
ISBN : 9783642335969

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Mechanics of Advanced Functional Materials by Biao Wang Pdf

Mechanics of Advanced Functional Materials emphasizes the coupling effect between the electric and mechanical field in the piezoelectric, ferroelectric and other functional materials. It also discusses the size effect on the ferroelectric domain instability and phase transition behaviors using the continuum micro-structural evolution models. Functional materials usually have a very wide application in engineering due to their unique thermal, electric, magnetic, optoelectronic, etc., functions. Almost all the applications demand that the material should have reasonable stiffness, strength, fracture toughness and the other mechanical properties. Furthermore, usually the stress and strain fields on the functional materials and devices have some important coupling effect on the functionality of the materials. Much progress has been made concerning the coupling electric and mechanical behaviors such as the coupled electric and stress field distribution in piezoelectric solids, ferroelectric domain patterns in ferroelectrics, fracture and failure properties under coupled electric and stress field, etc. The book is intended for researchers and postgraduate students in the fields of mechanics, materials sciences and applied physics who are interested to work on the interdisciplinary mathematical modeling of the functional materials. Prof. Biao Wang is the Dean of School of Physics and Engineering of the Sun Yat-sen University, China.

Studies in Evolution Equations and Related Topics

Gaston M. N'Guérékata,Bourama Toni
Studies in Evolution Equations and Related Topics Book PDF

Author : Gaston M. N'Guérékata,Bourama Toni
Publisher : Springer Nature
Page : 275 pages
File Size : 54,8 Mb
Release : 2021-10-27
Category : Mathematics
ISBN : 9783030777043

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Studies in Evolution Equations and Related Topics by Gaston M. N'Guérékata,Bourama Toni Pdf

This volume features recent development and techniques in evolution equations by renown experts in the field. Each contribution emphasizes the relevance and depth of this important area of mathematics and its expanding reach into the physical, biological, social, and computational sciences as well as into engineering and technology. The reader will find an accessible summary of a wide range of active research topics, along with exciting new results. Topics include: Impulsive implicit Caputo fractional q-difference equations in finite and infinite dimensional Banach spaces; optimal control of averaged state of a population dynamic model; structural stability of nonlinear elliptic p(u)-Laplacian problem with Robin-type boundary condition; exponential dichotomy and partial neutral functional differential equations, stable and center-stable manifolds of admissible class; global attractor in Alpha-norm for some partial functional differential equations of neutral and retarded type; and more. Researchers in mathematical sciences, biosciences, computational sciences and related fields, will benefit from the rich and useful resources provided. Upper undergraduate and graduate students may be inspired to contribute to this active and stimulating field.

Delay Differential Evolutions Subjected to Nonlocal Initial Conditions

Monica-Dana Burlică,Mihai Necula,Daniela Roșu,Ioan I. Vrabie
Delay Differential Evolutions Subjected to Nonlocal Initial Conditions Book PDF

Author : Monica-Dana Burlică,Mihai Necula,Daniela Roșu,Ioan I. Vrabie
Publisher : CRC Press
Page : 322 pages
File Size : 50,9 Mb
Release : 2018-09-03
Category : Mathematics
ISBN : 9781315351681

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Delay Differential Evolutions Subjected to Nonlocal Initial Conditions by Monica-Dana Burlică,Mihai Necula,Daniela Roșu,Ioan I. Vrabie Pdf

Filling a gap in the literature, Delay Differential Evolutions Subjected to Nonlocal Initial Conditions reveals important results on ordinary differential equations (ODEs) and partial differential equations (PDEs). It presents very recent results relating to the existence, boundedness, regularity, and asymptotic behavior of global solutions for differential equations and inclusions, with or without delay, subjected to nonlocal implicit initial conditions. After preliminaries on nonlinear evolution equations governed by dissipative operators, the book gives a thorough study of the existence, uniqueness, and asymptotic behavior of global bounded solutions for differential equations with delay and local initial conditions. It then focuses on two important nonlocal cases: autonomous and quasi-autonomous. The authors next discuss sufficient conditions for the existence of almost periodic solutions, describe evolution systems with delay and nonlocal initial conditions, examine delay evolution inclusions, and extend some results to the multivalued case of reaction-diffusion systems. The book concludes with results on viability for nonlocal evolution inclusions.