Fractional Evolution Equations and Inclusions Book

Fractional Evolution Equations and Inclusions


  • Author : Yong Zhou
  • Publisher : Academic Press
  • Release Date : 2016-02-05
  • Genre: Mathematics
  • Pages : 294
  • ISBN 10 : 9780128047750

DOWNLOAD BOOK
Fractional Evolution Equations and Inclusions 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

Fractional Order Equations and Inclusions Book

Fractional Order Equations and Inclusions


  • Author : Michal Fečkan
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release Date : 2017-11-07
  • Genre: Mathematics
  • Pages : 383
  • ISBN 10 : 9783110521559

DOWNLOAD BOOK
Fractional Order Equations and Inclusions Excerpt :

This book presents fractional difference, integral, differential, evolution equations and inclusions, and discusses existence and asymptotic behavior of their solutions. Controllability and relaxed control results are obtained. Combining rigorous deduction with abundant examples, it is of interest to nonlinear science researchers using fractional equations as a tool, and physicists, mechanics researchers and engineers studying relevant topics. Contents Fractional Difference Equations Fractional Integral Equations Fractional Differential Equations Fractional Evolution Equations: Continued Fractional Differential Inclusions

Theory of Fractional Evolution Equations Book

Theory of Fractional Evolution Equations


  • Author : Yong Zhou
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release Date : 2022-03-21
  • Genre: Mathematics
  • Pages : 342
  • ISBN 10 : 9783110769272

DOWNLOAD BOOK
Theory of Fractional Evolution Equations 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.

Fractional Differential Equations  Inclusions and Inequalities with Applications Book

Fractional Differential Equations Inclusions and Inequalities with Applications


  • Author : Sotiris K. Ntouyas
  • Publisher : MDPI
  • Release Date : 2020-11-09
  • Genre: Mathematics
  • Pages : 518
  • ISBN 10 : 9783039432189

DOWNLOAD BOOK
Fractional Differential Equations Inclusions and Inequalities with Applications 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.

Theory of Fractional Evolution Equations Book

Theory of Fractional Evolution Equations


  • Author : Yong Zhou
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release Date : 2022-03-21
  • Genre: Mathematics
  • Pages : 342
  • ISBN 10 : 9783110769364

DOWNLOAD BOOK
Theory of Fractional Evolution Equations 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.

Studies in Evolution Equations and Related Topics Book

Studies in Evolution Equations and Related Topics


  • Author : Gaston M. N'Guérékata
  • Publisher : Springer Nature
  • Release Date : 2021-10-27
  • Genre: Mathematics
  • Pages : 268
  • ISBN 10 : 9783030777043

DOWNLOAD BOOK
Studies in Evolution Equations and Related Topics Excerpt :

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.

Bloch type Periodic Functions  Theory And Applications To Evolution Equations Book

Bloch type Periodic Functions Theory And Applications To Evolution Equations


  • Author : Yong-kui Chang
  • Publisher : World Scientific
  • Release Date : 2022-07-13
  • Genre: Mathematics
  • Pages : 209
  • ISBN 10 : 9789811254376

DOWNLOAD BOOK
Bloch type Periodic Functions Theory And Applications To Evolution Equations Excerpt :

This monograph aims to provide for the first time a unified and homogenous presentation of the recent works on the theory of Bloch periodic functions, their generalizations, and their applications to evolution equations. It is useful for graduate students and beginning researchers as seminar topics, graduate courses and reference text in pure and applied mathematics, physics, and engineering.

Fractional Calculus Book

Fractional Calculus


  • Author : Praveen Agarwal
  • Publisher : Springer Nature
  • Release Date : 2019-11-23
  • Genre: Mathematics
  • Pages : 249
  • ISBN 10 : 9789811504303

DOWNLOAD BOOK
Fractional Calculus Excerpt :

This book collects papers presented at the International Conference on Fractional Differentiation and its Applications (ICFDA), held at the University of Jordan, Amman, Jordan, on 16–18 July 2018. Organized into 13 chapters, the book discusses the latest trends in various fields of theoretical and applied fractional calculus. Besides an essential mathematical interest, its overall goal is a general improvement of the physical world models for the purpose of computer simulation, analysis, design and control in practical applications. It showcases the development of fractional calculus as an acceptable tool for a large number of diverse scientific communities due to more adequate modeling in various fields of mechanics, electricity, chemistry, biology, medicine, economics, control theory, as well as signal and image processing. The book will be a valuable resource for graduate students and researchers of mathematics and engineering.

Mathematical Techniques of Fractional Order Systems Book

Mathematical Techniques of Fractional Order Systems


  • Author : Ahmad Taher Azar
  • Publisher : Elsevier
  • Release Date : 2018-06-11
  • Genre: Technology & Engineering
  • Pages : 700
  • ISBN 10 : 9780128135938

DOWNLOAD BOOK
Mathematical Techniques of Fractional Order Systems Excerpt :

Mathematical Techniques of Fractional Order Systems illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order circuit theorems from different perspectives in design, analysis and realizations, nonlinear fractional-order circuits and systems, the fractional-order memristive circuits and systems in design, analysis, emulators, simulation and experimental results. It is primarily meant for researchers from academia and industry, and for those working in areas such as control engineering, electrical engineering, computer science and information technology. This book is ideal for researchers working in the area of both continuous-time and discrete-time dynamics and chaotic systems. Discusses multidisciplinary applications with new fundamentals, modeling, analysis, design, realization and experimental results Includes circuits and systems based on new nonlinear elements Covers most of the linear and nonlinear fractional-order theorems that will solve many scientific issues for researchers Closes the gap between theoretical approaches and real-world applications Provides MATLAB® and Simulink code for many applications in the book

Automatic Control  Robotics  and Information Processing Book

Automatic Control Robotics and Information Processing


  • Author : Piotr Kulczycki
  • Publisher : Springer Nature
  • Release Date : 2020-09-03
  • Genre: Technology & Engineering
  • Pages : 843
  • ISBN 10 : 9783030485870

DOWNLOAD BOOK
Automatic Control Robotics and Information Processing Excerpt :

This book presents a wide and comprehensive range of issues and problems in various fields of science and engineering, from both theoretical and applied perspectives. The desire to develop more effective and efficient tools and techniques for dealing with complex processes and systems has been a natural inspiration for the emergence of numerous fields of science and technology, in particular control and automation and, more recently, robotics. The contributions gathered here concern the development of methods and algorithms to determine best practices regarding broadly perceived decisions or controls. From an engineering standpoint, many of them focus on how to automate a specific process or complex system. From a tools-based perspective, several contributions address the development of analytic and algorithmic methods and techniques, devices and systems that make it possible to develop and subsequently implement the automation and robotization of crucial areas of human activity. All topics discussed are illustrated with sample applications.

Fractional Differential Equations Book

Fractional Differential Equations


  • Author : Anatoly Kochubei
  • Publisher : Walter de Gruyter GmbH & Co KG
  • Release Date : 2019-02-19
  • Genre: Mathematics
  • Pages : 527
  • ISBN 10 : 9783110571660

DOWNLOAD BOOK
Fractional Differential Equations Excerpt :

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.

Basic Theory of Fractional Differential Equations Book

Basic Theory of Fractional Differential Equations


  • Author : Yong Zhou
  • Publisher : World Scientific
  • Release Date : 2016-10-20
  • Genre: Mathematics
  • Pages : 380
  • ISBN 10 : 9789813148185

DOWNLOAD BOOK
Basic Theory of Fractional Differential Equations 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. Contents:Preliminaries:IntroductionSome Notations, Concepts and LemmasFractional CalculusSome Results from Nonlinear AnalysisSemigroupsFractional Functional Differential Equations:IntroductionNeutral Equations with Bounded Delayp-Type Neutral EquationsNeutral Equations with Infinite DelayIterative Functional Differential EquationsNotes and RemarksFractional Ordinary Differential Equations in Banach Spaces:IntroductionCauchy Problems via Measure of Noncompactness MethodCauchy Problems via Topological Degree MethodCauchy Problems via Picard Operators TechniqueNotes and RemarksFractional Abstract Evolution Equations:IntroductionEvolution Equations with Riemann–Liouville DerivativeEvolution Equations with Caputo DerivativeNonlocal Problems for Evolution EquationsAbstract Cauchy Problems with Almost Sectorial OperatorsNotes and RemarksFractional Impulsive Differential Equations:IntroductionImpulsive Initial Value ProblemsImpulsive Boundary Value ProblemsImpulsive Langevin EquationsImpulsive Evolution EquationsNotes and RemarksFractional Boundary Value Problem

Nonlinear Differential Equations and Dynamical Systems Book

Nonlinear Differential Equations and Dynamical Systems


  • Author : Feliz Manuel Minhós
  • Publisher : MDPI
  • Release Date : 2021-04-15
  • Genre: Mathematics
  • Pages : 158
  • ISBN 10 : 9783036507101

DOWNLOAD BOOK
Nonlinear Differential Equations and Dynamical Systems Excerpt :

This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.

Evolution Equations Book

Evolution Equations


  • Author : Kaïs Ammari
  • Publisher : Cambridge University Press
  • Release Date : 2018
  • Genre: Mathematics
  • Pages : 205
  • ISBN 10 : 9781108412308

DOWNLOAD BOOK
Evolution Equations Excerpt :

The proceedings of a summer school held in 2015 whose theme was long time behavior and control of evolution equations.