Fractional Order 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 : 45,7 Mb
Release : 2017-11-07
Category : Mathematics
ISBN : 9783110522075

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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 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 : 48,9 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 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 : 53,7 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.

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 : 54,6 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.

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 : 51,6 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. ​

Recent Investigations of Differential and Fractional Equations and Inclusions

Snezhana Hristova
Recent Investigations of Differential and Fractional Equations and Inclusions Book PDF

Author : Snezhana Hristova
Publisher : MDPI
Page : 190 pages
File Size : 55,6 Mb
Release : 2021-02-22
Category : Mathematics
ISBN : 9783036500744

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Recent Investigations of Differential and Fractional Equations and Inclusions by Snezhana Hristova Pdf

During the past decades, the subject of calculus of integrals and derivatives of any arbitrary real or complex order has gained considerable popularity and impact. This is mainly due to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. In connection with this, great importance is attached to the publication of results that focus on recent and novel developments in the theory of any types of differential and fractional differential equation and inclusions, especially covering analytical and numerical research for such kinds of equations. This book is a compilation of articles from a Special Issue of Mathematics devoted to the topic of “Recent Investigations of Differential and Fractional Equations and Inclusions”. It contains some theoretical works and approximate methods in fractional differential equations and inclusions as well as fuzzy integrodifferential equations. Many of the papers were supported by the Bulgarian National Science Fund under Project KP-06-N32/7. Overall, the volume is an excellent witness of the relevance of the theory of 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 : 51,5 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

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 : 50,9 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

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 : 52,5 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.

Nonlocal Nonlinear Fractional-order Boundary Value Problems

Bashir Ahmad,Sotiris K Ntouyas
Nonlocal Nonlinear Fractional order Boundary Value Problems Book PDF

Author : Bashir Ahmad,Sotiris K Ntouyas
Publisher : World Scientific
Page : 597 pages
File Size : 50,6 Mb
Release : 2021-04-06
Category : Mathematics
ISBN : 9789811230424

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Nonlocal Nonlinear Fractional-order Boundary Value Problems by Bashir Ahmad,Sotiris K Ntouyas Pdf

There has been a great advancement in the study of fractional-order nonlocal nonlinear boundary value problems during the last few decades. The interest in the subject of fractional-order boundary value problems owes to the extensive application of fractional differential equations in many engineering and scientific disciplines. Fractional-order differential and integral operators provide an excellent instrument for the description of memory and hereditary properties of various materials and processes, which contributed significantly to the popularity of the subject and motivated many researchers and modelers to shift their focus from classical models to fractional order models. Some peculiarities of physical, chemical or other processes happening inside the domain cannot be formulated with the aid of classical boundary conditions. This limitation led to the consideration of nonlocal and integral conditions which relate the boundary values of the unknown function to its values at some interior positions of the domain.The main objective for writing this book is to present some recent results on single-valued and multi-valued boundary value problems, involving different kinds of fractional differential and integral operators, and several kinds of nonlocal multi-point, integral, integro-differential boundary conditions. Much of the content of this book contains the recent research published by the authors on the topic.

Recent Investigations of Differential and Fractional Equations and Inclusions

Snezhana Hristova
Recent Investigations of Differential and Fractional Equations and Inclusions Book PDF

Author : Snezhana Hristova
Publisher : Unknown
Page : 190 pages
File Size : 54,7 Mb
Release : 2021
Category : Electronic
ISBN : 3036500758

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Recent Investigations of Differential and Fractional Equations and Inclusions by Snezhana Hristova Pdf

During the past decades, the subject of calculus of integrals and derivatives of any arbitrary real or complex order has gained considerable popularity and impact. This is mainly due to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. In connection with this, great importance is attached to the publication of results that focus on recent and novel developments in the theory of any types of differential and fractional differential equation and inclusions, especially covering analytical and numerical research for such kinds of equations. This book is a compilation of articles from a Special Issue of Mathematics devoted to the topic of “Recent Investigations of Differential and Fractional Equations and Inclusions”. It contains some theoretical works and approximate methods in fractional differential equations and inclusions as well as fuzzy integrodifferential equations. Many of the papers were supported by the Bulgarian National Science Fund under Project KP-06-N32/7. Overall, the volume is an excellent witness of the relevance of the theory of fractional differential equations.

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 : 43,6 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

Generalized Fractional Order Differential Equations Arising in Physical Models

Santanu Saha Ray,Subhadarshan Sahoo
Generalized Fractional Order Differential Equations Arising in Physical Models Book PDF

Author : Santanu Saha Ray,Subhadarshan Sahoo
Publisher : CRC Press
Page : 351 pages
File Size : 42,9 Mb
Release : 2018-11-13
Category : Mathematics
ISBN : 9780429771798

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Generalized Fractional Order Differential Equations Arising in Physical Models by Santanu Saha Ray,Subhadarshan Sahoo Pdf

This book analyzes the various semi-analytical and analytical methods for finding approximate and exact solutions of fractional order partial differential equations. It explores approximate and exact solutions obtained by various analytical methods for fractional order partial differential equations arising in physical models.

Impulsive Differential Inclusions

John R. Graef,Johnny Henderson,Abdelghani Ouahab
Impulsive Differential Inclusions Book PDF

Author : John R. Graef,Johnny Henderson,Abdelghani Ouahab
Publisher : Walter de Gruyter
Page : 412 pages
File Size : 51,9 Mb
Release : 2013-07-31
Category : Mathematics
ISBN : 9783110295313

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Impulsive Differential Inclusions by John R. Graef,Johnny Henderson,Abdelghani Ouahab Pdf

Differential equations with impulses arise as models of many evolving processes that are subject to abrupt changes, such as shocks, harvesting, and natural disasters. These phenomena involve short-term perturbations from continuous and smooth dynamics, whose duration is negligible in comparison with the duration of an entire evolution. In models involving such perturbations, it is natural to assume these perturbations act instantaneously or in the form of impulses. As a consequence, impulsive differential equations have been developed in modeling impulsive problems in physics, population dynamics, ecology, biotechnology, industrial robotics, pharmacokinetics, optimal control, and so forth. There are also many different studies in biology and medicine for which impulsive differential equations provide good models. During the last 10 years, the authors have been responsible for extensive contributions to the literature on impulsive differential inclusions via fixed point methods. This book is motivated by that research as the authors endeavor to bring under one cover much of those results along with results by other researchers either affecting or affected by the authors' work. The questions of existence and stability of solutions for different classes of initial value problems for impulsive differential equations and inclusions with fixed and variable moments are considered in detail. Attention is also given to boundary value problems. In addition, since differential equations can be viewed as special cases of differential inclusions, significant attention is also given to relative questions concerning differential equations. This monograph addresses a variety of side issues that arise from its simpler beginnings as well.

Mathematical Techniques of Fractional Order Systems

Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan
Mathematical Techniques of Fractional Order Systems Book PDF

Author : Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan
Publisher : Elsevier
Page : 700 pages
File Size : 46,5 Mb
Release : 2018-06-11
Category : Technology & Engineering
ISBN : 9780128135938

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Mathematical Techniques of Fractional Order Systems by Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan Pdf

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