Fractional Difference Differential Equations And Inclusions

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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 : 50,8 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.

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 : 53,5 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 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 : 55,7 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, Inclusions and Inequalities with Applications

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

Author : Sotiris K. Ntouyas
Publisher : Unknown
Page : 518 pages
File Size : 42,5 Mb
Release : 2020
Category : Electronic
ISBN : 3039432192

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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.

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 : 40,9 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.

Topological Methods for Differential Equations and Inclusions

John R. Graef,Johnny Henderson,Abdelghani Ouahab
Topological Methods for Differential Equations and Inclusions Book PDF

Author : John R. Graef,Johnny Henderson,Abdelghani Ouahab
Publisher : CRC Press
Page : 360 pages
File Size : 55,9 Mb
Release : 2018-09-25
Category : Mathematics
ISBN : 9780429822629

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Topological Methods for Differential Equations and Inclusions by John R. Graef,Johnny Henderson,Abdelghani Ouahab Pdf

Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis.

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 : 52,9 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. ​

Fractional Differential Equations

Igor Podlubny
Fractional Differential Equations Book PDF

Author : Igor Podlubny
Publisher : Elsevier
Page : 366 pages
File Size : 52,9 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

Fractional Differential Equations

Zhi-Zhong Sun,Guang-hua Gao
Fractional Differential Equations Book PDF

Author : Zhi-Zhong Sun,Guang-hua Gao
Publisher : Walter de Gruyter GmbH & Co KG
Page : 226 pages
File Size : 45,5 Mb
Release : 2020-08-24
Category : Mathematics
ISBN : 9783110615302

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Fractional Differential Equations by Zhi-Zhong Sun,Guang-hua Gao Pdf

Starting with an introduction to fractional derivatives and numerical approximations, this book presents finite difference methods for fractional differential equations, including time-fractional sub-diffusion equations, time-fractional wave equations, and space-fractional differential equations, among others. Approximation methods for fractional derivatives are developed and approximate accuracies are analyzed in detail.

Fractional Partial Differential Equations and Their Numerical Solutions

Boling Guo,Xueke Pu,Fenghui Huang
Fractional Partial Differential Equations and Their Numerical Solutions Book PDF

Author : Boling Guo,Xueke Pu,Fenghui Huang
Publisher : World Scientific
Page : 348 pages
File Size : 51,5 Mb
Release : 2015-03-09
Category : Mathematics
ISBN : 9789814667067

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Fractional Partial Differential Equations and Their Numerical Solutions by Boling Guo,Xueke Pu,Fenghui Huang Pdf

This book aims to introduce some new trends and results on the study of the fractional differential equations, and to provide a good understanding of this field to beginners who are interested in this field, which is the authors' beautiful hope. This book describes theoretical and numerical aspects of the fractional partial differential equations, including the authors' researches in this field, such as the fractional Nonlinear Schrödinger equations, fractional Landau–Lifshitz equations and fractional Ginzburg–Landau equations. It also covers enough fundamental knowledge on the fractional derivatives and fractional integrals, and enough background of the fractional PDEs. Contents:Physics BackgroundFractional Calculus and Fractional Differential EquationsFractional Partial Differential EquationsNumerical Approximations in Fractional CalculusNumerical Methods for the Fractional Ordinary Differential EquationsNumerical Methods for Fractional Partial Differential Equations Readership: Graduate students and researchers in mathematical physics, numerical analysis and computational mathematics. Key Features:This book covers the fundamentals of this field, especially for the beginnersThe book covers new trends and results in this fieldThe book covers numerical results, which will be of broad interests to researchersKeywords:Fractional Partial Differential Equations;Numerical Solutions

Boundary Value Problems for Systems of Differential, Difference and Fractional Equations

Johnny Henderson,Rodica Luca
Boundary Value Problems for Systems of Differential Difference and Fractional Equations Book PDF

Author : Johnny Henderson,Rodica Luca
Publisher : Academic Press
Page : 322 pages
File Size : 54,5 Mb
Release : 2015-10-30
Category : Mathematics
ISBN : 9780128036792

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Boundary Value Problems for Systems of Differential, Difference and Fractional Equations by Johnny Henderson,Rodica Luca Pdf

Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions discusses the concept of a differential equation that brings together a set of additional constraints called the boundary conditions. As boundary value problems arise in several branches of math given the fact that any physical differential equation will have them, this book will provide a timely presentation on the topic. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed. Explains the systems of second order and higher orders differential equations with integral and multi-point boundary conditions Discusses second order difference equations with multi-point boundary conditions Introduces Riemann-Liouville fractional differential equations with uncoupled and coupled integral boundary conditions

Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities

Bashir Ahmad,Ahmed Alsaedi,Sotiris K. Ntouyas,Jessada Tariboon
Hadamard Type Fractional Differential Equations Inclusions and Inequalities Book PDF

Author : Bashir Ahmad,Ahmed Alsaedi,Sotiris K. Ntouyas,Jessada Tariboon
Publisher : Springer
Page : 414 pages
File Size : 50,8 Mb
Release : 2017-03-16
Category : Mathematics
ISBN : 9783319521411

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Hadamard-Type Fractional Differential Equations, Inclusions and Inequalities by Bashir Ahmad,Ahmed Alsaedi,Sotiris K. Ntouyas,Jessada Tariboon Pdf

This book focuses on the recent development of fractional differential equations, integro-differential equations, and inclusions and inequalities involving the Hadamard derivative and integral. Through a comprehensive study based in part on their recent research, the authors address the issues related to initial and boundary value problems involving Hadamard type differential equations and inclusions as well as their functional counterparts. The book covers fundamental concepts of multivalued analysis and introduces a new class of mixed initial value problems involving the Hadamard derivative and Riemann-Liouville fractional integrals. In later chapters, the authors discuss nonlinear Langevin equations as well as coupled systems of Langevin equations with fractional integral conditions. Focused and thorough, this book is a useful resource for readers and researchers interested in the area of fractional calculus.

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 : 40,5 Mb
Release : 2018-02-05
Category : Mathematics
ISBN : 9783110553819

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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. ContentsPreliminary 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

Introduction to the Theory of Differential Inclusions

Georgi V. Smirnov
Introduction to the Theory of Differential Inclusions Book PDF

Author : Georgi V. Smirnov
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 40,6 Mb
Release : 2002
Category : Mathematics
ISBN : 1470420929

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Introduction to the Theory of Differential Inclusions by Georgi V. Smirnov Pdf

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. This text acts as an introduction to the subject.

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 : 49,6 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.