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.
Sample Chapter(s)
Preface to the Third Edition
Chapter 2: Fractional Functional Differential Equations
Contents:
- Preface to the Third Edition
- About the Author
- Fractional Functional Differential Equations
- Fractional Ordinary Differential Equations in Banach Spaces
- Fractional Abstract Evolution Equations
- Fractional Impulsive Differential Equations
- Fractional Boundary Value Problems
- Fractional Hamiltonian Systems
- Fractional Partial Differential Equations
- Bibliography
- Index
Readership: Researchers and graduate students dealing with fractional calculus and applied analysis, differential equations and related areas for research, seminars, and advanced graduate courses, in pure and applied mathematics, physics, mechanics, engineering, biology, and related disciplines.
Reviews of the First Edition:
"The book is a good resource to familiarize oneself with current achievements in the theory of fractional differential equations of various types. It is well written, and every chapter is equipped with an interesting introduction."
Mathematical Reviews Clippings
"The last chapter of this book is devoted to fractional partial differential equations. It is very useful for readers who want to do theoretical work in this area."
Zentralblatt MATH
Yong Zhou is a Professor of the Faculty of Mathematics and Computational Science at Xiangtan University since 2000. He is also a Distinguished Guest Professor of Macau University of Science and Technology since 2018. His research fields include fractional differential equations, functional differential equations, evolution equations and inclusions, control theory. Zhou has published six monographs with Springer, World Scientific, Elsevier, De Gruyter and Science Press respectively, and more than three hundred research papers. He was included in the Highly Cited Researchers list from Thompson Reuters (2014) and Clarivate Analytics (2015–2021). Zhou has undertaken five projects from the National Natural Science Foundation of China. He was the Editor-in-Chief of International Journal of Dynamical Systems and Differential Equations from 2007 to 2011. In addition, he had worked as an Associate Editor for IEEE Transactions on Fuzzy Systems, and an Editorial Board Member of Fractional Calculus and Applied Analysis.