Topics In Fractional Differential Equations

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Topics In Fractional Differential Equations

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Author : Saïd Abbas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-17

Topics In Fractional Differential Equations written by Saïd Abbas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-17 with Mathematics categories.

​​​ 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. ​

The Analysis Of Fractional Differential Equations

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Author : Kai Diethelm
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-03

The Analysis Of Fractional Differential Equations written by Kai Diethelm and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-03 with Mathematics categories.

Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.

Advanced Topics In Fractional Differential Equations

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Author : Mouffak Benchohra
language : en
Publisher: Springer Nature
Release Date : 2023-05-11

Advanced Topics In Fractional Differential Equations written by Mouffak Benchohra and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-11 with Mathematics categories.

This book explores fractional differential equations with a fixed point approach. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations. All of the problems in the book also deal with some form of of the well-known Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. Classical and new fixed point theorems, associated with the measure of noncompactness in Banach spaces as well as several generalizations of the Gronwall's lemma, are employed as tools. The book is based on many years of research in this area, and provides suggestions for further study as well. The authors have included illustrations in order to support the readers’ understanding of the concepts presented. Includes illustrations in order to support readers understanding of the presented concepts · Approaches the topic of fractional differential equations while employing fixed point theorems as tools · Presents novel results, which build upon previous literature and many years of research by the authors

Basic Theory Of Fractional Differential Equations Third Edition

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Author : Yong Zhou
language : en
Publisher: World Scientific
Release Date : 2023-10-06

Basic Theory Of Fractional Differential Equations Third Edition written by Yong Zhou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-06 with Mathematics categories.

This accessible monograph is devoted to a rapidly developing area on the research of qualitative theory of fractional ordinary differential equations and evolution equations. It is self-contained and unified in presentation, and provides the readers the necessary background material required to go further into the subject and explore the rich research literature. The tools used include many classical and modern nonlinear analysis methods such as fixed point theory, measure of noncompactness method, topological degree method, Picard operators technique, critical point theory and semigroups theory. This book is based on the research work done so far by the author and other experts, and contains comprehensive up-to-date materials on the topic.In this third edition, four new topics have been added: Hilfer fractional evolution equations and infinite interval problems, oscillations and nonoscillations, fractional Hamiltonian systems, fractional Rayleigh-Stokes equations, and wave equations. The bibliography has also been updated and expanded.This book is useful to researchers, graduate or PhD students dealing with fractional calculus and applied analysis, differential equations, and related areas of research.

Fractional Differential Equations

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Author : Bangti Jin
language : en
Publisher: Springer Nature
Release Date : 2021-07-22

Fractional Differential Equations written by Bangti Jin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-22 with Mathematics categories.

This graduate textbook provides a self-contained introduction to modern mathematical theory on fractional differential equations. It addresses both ordinary and partial differential equations with a focus on detailed solution theory, especially regularity theory under realistic assumptions on the problem data. The text includes an extensive bibliography, application-driven modeling, extensive exercises, and graphic illustrations throughout to complement its comprehensive presentation of the field. It is recommended for graduate students and researchers in applied and computational mathematics, particularly applied analysis, numerical analysis and inverse problems.

Fractional Calculus And Fractional Differential Equations

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Author : Varsha Daftardar-Gejji
language : en
Publisher: Springer
Release Date : 2019-08-10

Fractional Calculus And Fractional Differential Equations written by Varsha Daftardar-Gejji and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-10 with Mathematics categories.

This book provides a broad overview of the latest developments in fractional calculus and fractional differential equations (FDEs) with an aim to motivate the readers to venture into these areas. It also presents original research describing the fractional operators of variable order, fractional-order delay differential equations, chaos and related phenomena in detail. Selected results on the stability of solutions of nonlinear dynamical systems of the non-commensurate fractional order have also been included. Furthermore, artificial neural network and fractional differential equations are elaborated on; and new transform methods (for example, Sumudu methods) and how they can be employed to solve fractional partial differential equations are discussed. The book covers the latest research on a variety of topics, including: comparison of various numerical methods for solving FDEs, the Adomian decomposition method and its applications to fractional versions of the classical Poisson processes, variable-order fractional operators, fractional variational principles, fractional delay differential equations, fractional-order dynamical systems and stability analysis, inequalities and comparison theorems in FDEs, artificial neural network approximation for fractional operators, and new transform methods for solving partial FDEs. Given its scope and level of detail, the book will be an invaluable asset for researchers working in these areas.

Fractional Differential Equations

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Author : Igor Podlubny
language : en
Publisher: Elsevier
Release Date : 1998-10-27

Fractional Differential Equations written by Igor Podlubny and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-27 with Mathematics categories.

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 Order Equations And Inclusions

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Author : Michal Fečkan
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-11-07

Fractional Order Equations And Inclusions written by Michal Fečkan and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-07 with Mathematics categories.

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

Implicit Fractional Differential And Integral Equations

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Author : Saïd Abbas
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-02-05

Implicit Fractional Differential And Integral Equations written by Saïd Abbas and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-05 with Mathematics categories.

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. Contents Preliminary 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

Fuzzy Fractional Differential Operators And Equations

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Author : Tofigh Allahviranloo
language : en
Publisher: Springer Nature
Release Date : 2020-06-15

Fuzzy Fractional Differential Operators And Equations written by Tofigh Allahviranloo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-15 with Technology & Engineering categories.

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.