Fractional Evolution Equations And Inclusions

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Fractional-Order Equations and Inclusions

Michal Fečkan,JinRong Wang,Michal Pospíšil
Fractional Order Equations and Inclusions Book PDF

Author : Michal Fečkan,JinRong Wang,Michal Pospíšil
Publisher : Walter de Gruyter GmbH & Co KG
Page : 383 pages
File Size : 45,9 Mb
Release : 2017-11-07
Category : Mathematics
ISBN : 9783110521559

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Fractional-Order Equations and Inclusions by Michal Fečkan,JinRong Wang,Michal Pospíšil Pdf

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

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 : 44,7 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

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 : 41,9 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.

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 : 40,5 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.

Fractional Differential Equations, Inclusions and Inequalities with Applications

Sotiris K. Ntouyas
Fractional Differential Equations Inclusions and Inequalities with Applications Book PDF

Author : Sotiris K. Ntouyas
Publisher : MDPI
Page : 518 pages
File Size : 45,6 Mb
Release : 2020-11-09
Category : Mathematics
ISBN : 9783039432189

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Fractional Differential Equations, Inclusions and Inequalities with Applications by Sotiris K. Ntouyas Pdf

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.

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 : 43,6 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.

Nonautonomous Fractional Evolution Equations

Yong Zhou,Jia Wei He
Nonautonomous Fractional Evolution Equations Book PDF

Author : Yong Zhou,Jia Wei He
Publisher : Walter de Gruyter GmbH & Co KG
Page : 258 pages
File Size : 51,7 Mb
Release : 2024-07-01
Category : Mathematics
ISBN : 9783111391243

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Nonautonomous Fractional Evolution Equations by Yong Zhou,Jia Wei He Pdf

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.

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 : 49,8 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 Differential Equations

Igor Podlubny
Fractional Differential Equations Book PDF

Author : Igor Podlubny
Publisher : Elsevier
Page : 366 pages
File Size : 51,7 Mb
Release : 1998-10-27
Category : Mathematics
ISBN : 9780080531984

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Fractional Differential Equations by Igor Podlubny Pdf

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

Stabilization for Some Fractional-Evolution Systems

Kaïs Ammari,Fathi Hassine,Luc Robbiano
Stabilization for Some Fractional Evolution Systems Book PDF

Author : Kaïs Ammari,Fathi Hassine,Luc Robbiano
Publisher : Springer Nature
Page : 73 pages
File Size : 40,6 Mb
Release : 2022-10-19
Category : Mathematics
ISBN : 9783031173431

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Stabilization for Some Fractional-Evolution Systems by Kaïs Ammari,Fathi Hassine,Luc Robbiano Pdf

This brief provides unified methods for the stabilization of some fractional evolution systems, nicely complementing existing literature on fractional calculus. The volume is divided into three chapters, the first of which considers the stabilization for some abstract evolution equations with a fractional damping, the second of which validates the abstract results of chapter 1 on concrete examples, and the third of which studies the stabilization of fractional evolution systems with memory.

Fractional Calculus

Praveen Agarwal,Dumitru Baleanu,YangQuan Chen,Shaher Momani,José António Tenreiro Machado
Fractional Calculus Book PDF

Author : Praveen Agarwal,Dumitru Baleanu,YangQuan Chen,Shaher Momani,José António Tenreiro Machado
Publisher : Springer Nature
Page : 251 pages
File Size : 45,6 Mb
Release : 2019-11-23
Category : Mathematics
ISBN : 9789811504303

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Fractional Calculus by Praveen Agarwal,Dumitru Baleanu,YangQuan Chen,Shaher Momani,José António Tenreiro Machado Pdf

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.

Evolution Equations

Kaïs Ammari,Stéphane Gerbi
Evolution Equations Book PDF

Author : Kaïs Ammari,Stéphane Gerbi
Publisher : Cambridge University Press
Page : 205 pages
File Size : 52,8 Mb
Release : 2018
Category : Mathematics
ISBN : 9781108412308

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Evolution Equations by Kaïs Ammari,Stéphane Gerbi Pdf

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

Topics in Fractional Differential Equations

Saïd Abbas,Mouffak Benchohra,Gaston M. N'Guérékata
Topics in Fractional Differential Equations Book PDF

Author : Saïd Abbas,Mouffak Benchohra,Gaston M. N'Guérékata
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 48,9 Mb
Release : 2012-08-17
Category : Mathematics
ISBN : 9781461440369

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Topics in Fractional Differential Equations by Saïd Abbas,Mouffak Benchohra,Gaston M. N'Guérékata Pdf

​​​ 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. ​

Nonlinear Differential Equations and Dynamical Systems

Feliz Manuel Minhós,João Fialho
Nonlinear Differential Equations and Dynamical Systems Book PDF

Author : Feliz Manuel Minhós,João Fialho
Publisher : MDPI
Page : 158 pages
File Size : 41,9 Mb
Release : 2021-04-15
Category : Mathematics
ISBN : 9783036507101

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Nonlinear Differential Equations and Dynamical Systems by Feliz Manuel Minhós,João Fialho Pdf

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.

Fuzzy Fractional Differential Operators and Equations

Tofigh Allahviranloo
Fuzzy Fractional Differential Operators and Equations Book PDF

Author : Tofigh Allahviranloo
Publisher : Springer Nature
Page : 303 pages
File Size : 44,5 Mb
Release : 2020-06-15
Category : Technology & Engineering
ISBN : 9783030512729

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Fuzzy Fractional Differential Operators and Equations by Tofigh Allahviranloo Pdf

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.