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.
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 Inclusions And Inequalities With Applications
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Author : Sotiris K. Ntouyas
language : en
Publisher: MDPI
Release Date : 2020-11-09
Fractional Differential Equations Inclusions And Inequalities With Applications written by Sotiris K. Ntouyas and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-09 with Mathematics categories.
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.
New Trends In Fractional Differential Equations With Real World Applications In Physics
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Author : Jagdev Singh
language : en
Publisher: Frontiers Media SA
Release Date : 2020-12-30
New Trends In Fractional Differential Equations With Real World Applications In Physics written by Jagdev Singh and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-30 with Science categories.
This eBook is a collection of articles from a Frontiers Research Topic. Frontiers Research Topics are very popular trademarks of the Frontiers Journals Series: they are collections of at least ten articles, all centered on a particular subject. With their unique mix of varied contributions from Original Research to Review Articles, Frontiers Research Topics unify the most influential researchers, the latest key findings and historical advances in a hot research area! Find out more on how to host your own Frontiers Research Topic or contribute to one as an author by contacting the Frontiers Editorial Office: frontiersin.org/about/contact.
Fractional Differential Equations And Inclusions Classical And Advanced Topics
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Author : Said Abbas
language : en
Publisher: World Scientific
Release Date : 2023-02-02
Fractional Differential Equations And Inclusions Classical And Advanced Topics written by Said Abbas and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-02 with Mathematics categories.
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.
An Introduction To The Fractional Calculus And Fractional Differential Equations
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Author : Kenneth S. Miller
language : en
Publisher: Wiley-Interscience
Release Date : 1993-06-02
An Introduction To The Fractional Calculus And Fractional Differential Equations written by Kenneth S. Miller and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-06-02 with Mathematics categories.
Commences with the historical development of fractional calculus, its mathematical theory—particularly the Riemann-Liouville version. Numerous examples and theoretical applications of the theory are presented. Features topics associated with fractional differential equations. Discusses Weyl fractional calculus and some of its uses. Includes selected physical problems which lead to fractional differential or integral equations.
Fractional Order Analysis
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Author : Hemen Dutta
language : en
Publisher: John Wiley & Sons
Release Date : 2020-09-01
Fractional Order Analysis written by Hemen Dutta and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-01 with Mathematics categories.
A guide to the new research in the field of fractional order analysis Fractional Order Analysis contains the most recent research findings in fractional order analysis and its applications. The authors—noted experts on the topic—offer an examination of the theory, methods, applications, and the modern tools and techniques in the field of fractional order analysis. The information, tools, and applications presented can help develop mathematical methods and models with better accuracy. Comprehensive in scope, the book covers a range of topics including: new fractional operators, fractional derivatives, fractional differential equations, inequalities for different fractional derivatives and fractional integrals, fractional modeling related to transmission of Malaria, and dynamics of Zika virus with various fractional derivatives, and more. Designed to be an accessible text, several useful, relevant and connected topics can be found in one place, which is crucial for an understanding of the research problems of an applied nature. This book: Contains recent development in fractional calculus Offers a balance of theory, methods, and applications Puts the focus on fractional analysis and its interdisciplinary applications, such as fractional models for biological models Helps make research more relevant to real-life applications Written for researchers, professionals and practitioners, Fractional Order Analysis offers a comprehensive resource to fractional analysis and its many applications as well as information on the newest research.
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.
Time Fractional Differential Equations
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Author : Adam Kubica
language : en
Publisher: Springer Nature
Release Date : 2020-11-29
Time Fractional Differential Equations written by Adam Kubica and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-29 with Mathematics categories.
This book aims to establish a foundation for fractional derivatives and fractional differential equations. The theory of fractional derivatives enables considering any positive order of differentiation. The history of research in this field is very long, with its origins dating back to Leibniz. Since then, many great mathematicians, such as Abel, have made contributions that cover not only theoretical aspects but also physical applications of fractional calculus. The fractional partial differential equations govern phenomena depending both on spatial and time variables and require more subtle treatments. Moreover, fractional partial differential equations are highly demanded model equations for solving real-world problems such as the anomalous diffusion in heterogeneous media. The studies of fractional partial differential equations have continued to expand explosively. However we observe that available mathematical theory for fractional partial differential equations is not still complete. In particular, operator-theoretical approaches are indispensable for some generalized categories of solutions such as weak solutions, but feasible operator-theoretic foundations for wide applications are not available in monographs. To make this monograph more readable, we are restricting it to a few fundamental types of time-fractional partial differential equations, forgoing many other important and exciting topics such as stability for nonlinear problems. However, we believe that this book works well as an introduction to mathematical research in such vast fields.