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Fractional Evolution Equations And Inclusions

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Fractional Evolution Equations and Inclusions

Fractional Evolution Equations and Inclusions Book
Author : Yong Zhou
Publisher : Academic Press
Release : 2016-02-05
ISBN : 0128047755
Language : En, Es, Fr & De

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Book Description :

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

Fractional Order Equations and Inclusions

Fractional Order Equations and Inclusions Book
Author : Michal Fečkan,JinRong Wang,Michal Pospíšil
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2017-11-07
ISBN : 3110521555
Language : En, Es, Fr & De

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Book Description :

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

Theory of Fractional Evolution Equations Book
Author : Yong Zhou,Bashir Ahmad,Ahmed Alsaedi
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2022-03-21
ISBN : 3110769271
Language : En, Es, Fr & De

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Book Description :

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.

Theory of Fractional Evolution Equations

Theory of Fractional Evolution Equations Book
Author : Yong Zhou,Bashir Ahmad,Ahmed Alsaedi
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2022-03-21
ISBN : 3110769360
Language : En, Es, Fr & De

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Book Description :

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

Fractional Differential Equations  Inclusions and Inequalities with Applications Book
Author : Sotiris K. Ntouyas
Publisher : MDPI
Release : 2020-11-09
ISBN : 3039432184
Language : En, Es, Fr & De

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Book Description :

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.

Studies in Evolution Equations and Related Topics

Studies in Evolution Equations and Related Topics Book
Author : Gaston M. N'Guérékata,Bourama Toni
Publisher : Springer Nature
Release : 2021-10-27
ISBN : 3030777049
Language : En, Es, Fr & De

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Book Description :

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

Bloch type Periodic Functions  Theory And Applications To Evolution Equations Book
Author : Yong-kui Chang,Gaston Mandata N'guerekata,Rodrigo Ponce
Publisher : World Scientific
Release : 2022-07-13
ISBN : 9811254370
Language : En, Es, Fr & De

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Book Description :

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

Fractional Calculus Book
Author : Praveen Agarwal,Dumitru Baleanu,YangQuan Chen,Shaher Momani,José António Tenreiro Machado
Publisher : Springer Nature
Release : 2019-11-23
ISBN : 981150430X
Language : En, Es, Fr & De

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Book Description :

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

Mathematical Techniques of Fractional Order Systems Book
Author : Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan
Publisher : Elsevier
Release : 2018-06-11
ISBN : 012813593X
Language : En, Es, Fr & De

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Book Description :

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

Automatic Control  Robotics  and Information Processing Book
Author : Piotr Kulczycki,Józef Korbicz,Janusz Kacprzyk
Publisher : Springer Nature
Release : 2020-09-03
ISBN : 3030485870
Language : En, Es, Fr & De

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Book Description :

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

Fractional Differential Equations Book
Author : Igor Podlubny
Publisher : Elsevier
Release : 1998-10-27
ISBN : 9780080531984
Language : En, Es, Fr & De

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Book Description :

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

Fractional Differential Equations

Fractional Differential Equations Book
Author : Anatoly Kochubei,Yuri Luchko
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2019-02-19
ISBN : 3110571668
Language : En, Es, Fr & De

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Book Description :

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.

Nonlinear Differential Equations and Dynamical Systems

Nonlinear Differential Equations and Dynamical Systems Book
Author : Feliz Manuel Minhós,João Fialho
Publisher : MDPI
Release : 2021-04-15
ISBN : 3036507108
Language : En, Es, Fr & De

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Book Description :

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

Evolution Equations Book
Author : Kaïs Ammari,Stéphane Gerbi
Publisher : Cambridge University Press
Release : 2018
ISBN : 1108412300
Language : En, Es, Fr & De

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Book Description :

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

Differential and Difference Equations with Applications

Differential and Difference Equations with Applications Book
Author : Sandra Pinelas,John R. Graef,Stefan Hilger,Peter Kloeden,Christos Schinas
Publisher : Springer Nature
Release : 2020-10-21
ISBN : 3030563235
Language : En, Es, Fr & De

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Book Description :

This edited volume gathers selected, peer-reviewed contributions presented at the fourth International Conference on Differential & Difference Equations Applications (ICDDEA), which was held in Lisbon, Portugal, in July 2019. First organized in 2011, the ICDDEA conferences bring together mathematicians from various countries in order to promote cooperation in the field, with a particular focus on applications. The book includes studies on boundary value problems; Markov models; time scales; non-linear difference equations; multi-scale modeling; and myriad applications.

Topics in Fractional Differential Equations

Topics in Fractional Differential Equations Book
Author : Saïd Abbas,Mouffak Benchohra,Gaston M. N'Guérékata
Publisher : Springer Science & Business Media
Release : 2012-08-17
ISBN : 146144036X
Language : En, Es, Fr & De

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Book Description :

​​​ Topics in Fractional Differential Equations is devoted to the existence and uniqueness of solutions for various classes of Darboux problems for hyperbolic differential equations or inclusions involving the Caputo fractional derivative. ​​Fractional calculus generalizes the integrals and derivatives to non-integer orders. During the last decade, fractional calculus was found to play a fundamental role in the modeling of a considerable number of phenomena; in particular the modeling of memory-dependent and complex media such as porous media. It has emerged as an important tool for the study of dynamical systems where classical methods reveal strong limitations. Some equations present delays which may be finite, infinite, or state-dependent. Others are subject to an impulsive effect. The above problems are studied using the fixed point approach, the method of upper and lower solution, and the Kuratowski measure of noncompactness. This book is addressed to a wide audience of specialists such as mathematicians, engineers, biologists, and physicists. ​

Fuzzy Fractional Differential Operators and Equations

Fuzzy Fractional Differential Operators and Equations Book
Author : Tofigh Allahviranloo
Publisher : Springer Nature
Release : 2020-06-15
ISBN : 303051272X
Language : En, Es, Fr & De

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Book Description :

This book contains new and useful materials concerning fuzzy fractional differential and integral operators and their relationship. As the title of the book suggests, the fuzzy subject matter is one of the most important tools discussed. Therefore, it begins by providing a brief but important and new description of fuzzy sets and the computational calculus they require. Fuzzy fractals and fractional operators have a broad range of applications in the engineering, medical and economic sciences. Although these operators have been addressed briefly in previous papers, this book represents the first comprehensive collection of all relevant explanations. Most of the real problems in the biological and engineering sciences involve dynamic models, which are defined by fuzzy fractional operators in the form of fuzzy fractional initial value problems. Another important goal of this book is to solve these systems and analyze their solutions both theoretically and numerically. Given the content covered, the book will benefit all researchers and students in the mathematical and computer sciences, but also the engineering sciences.

Selected Topics in Almost Periodicity

Selected Topics in Almost Periodicity Book
Author : Marko Kostić
Publisher : Walter de Gruyter GmbH & Co KG
Release : 2021-11-22
ISBN : 3110763524
Language : En, Es, Fr & De

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Book Description :

Covers uniformly recurrent solutions and c-almost periodic solutions of abstract Volterra integro-differential equations as well as various generalizations of almost periodic functions in Lebesgue spaces with variable coefficients. Treats multi-dimensional almost periodic type functions and their generalizations in adequate detail.

Evolution Equations

Evolution Equations Book
Author : Alexander Pankov
Publisher : Unknown
Release : 2018
ISBN : 9781536142587
Language : En, Es, Fr & De

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Book Description :

This volume of Advances in Evolution Equations is dedicated to the memory of Professor Vasilii Vasilievich Zhikov, an outstanding Russian mathematician. Zhikov's scientific interest ranged from almost periodic differential equations and topological dynamics to spectral theory of elliptic operators, qualitative theory of parabolic equations, calculus of variations, homogenization, and hydrodynamics, to name a few. Many of his results are now classical.

Functional Calculus

Functional Calculus Book
Author : Kamal Shah,Baver Okutmuştur
Publisher : BoD – Books on Demand
Release : 2020-06-17
ISBN : 1838800077
Language : En, Es, Fr & De

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Book Description :

The aim of this book is to present a broad overview of the theory and applications related to functional calculus. The book is based on two main subject areas: matrix calculus and applications of Hilbert spaces. Determinantal representations of the core inverse and its generalizations, new series formulas for matrix exponential series, results on fixed point theory, and chaotic graph operations and their fundamental group are contained under the umbrella of matrix calculus. In addition, numerical analysis of boundary value problems of fractional differential equations are also considered here. In addition, reproducing kernel Hilbert spaces, spectral theory as an application of Hilbert spaces, and an analysis of PM10 fluctuations and optimal control are all contained in the applications of Hilbert spaces. The concept of this book covers topics that will be of interest not only for students but also for researchers and professors in this field of mathematics. The authors of each chapter convey a strong emphasis on theoretical foundations in this book.