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.
Part I: Preliminaries.- Continuous Time Random Walk.- Fractional Calculus.- Mittag-Leffler and Wright Functions.- Part II: Fractional Ordinary Differential Equations.- Cauchy Problems for Fractional ODEs.- Boundary Value Problem for Fractional ODEs.- Part III: Time-Fractional Diffusion.- Subdiffusion: Hilbert Space Theory.- Subdiffusion: Hölder Space Theory.- Mathematical Preliminaries.- Index.
Bangti Jin received the B.Eng. degree in polymeric materials and engineering in 2002, theM.Sc. degree in computational mathematics in 2005, both from Zhejiang University, Hangzhou, China, and the Ph.D. degree in applied mathematics from the Chinese University of Hong Kong, Hong Kong, in 2008. Previously, he was an Assistant Professor of mathematics at the University of California, Riverside (2013-2014), a Visiting Assistant Professor at Texas A&M University (2010-2013), an Alexandre von Humboldt Postdoctoral Researcher at the University of Bremen (2009-2010). He is currently Professor of Inverse Problems at the Department of Computer Science, University College London, London, U.K. His research interests include computational inverse problems and numerical analysis of differential equations.
Über den Autor
Bangti Jin received the B.Eng. degree in polymeric materials and engineering in 2002, the
M.Sc. degree in computational mathematics in 2005, both from Zhejiang University, Hangzhou, China, and the Ph.D. degree in applied mathematics from the Chinese University of Hong Kong, Hong Kong, in 2008. Previously, he was an Assistant Professor of mathematics at the University of California, Riverside (2013-2014), a Visiting Assistant Professor at Texas A&M University (2010-2013), an Alexandre von Humboldt Postdoctoral Researcher at the University of Bremen (2009-2010). He is currently Professor of Inverse Problems at the Department of Computer Science, University College London, London, U.K. His research interests include computational inverse problems and numerical analysis of differential equations.
Inhaltsverzeichnis
Part I: Preliminaries.- Continuous Time Random Walk.- Fractional Calculus.- Mittag-Leffler and Wright Functions.- Part II: Fractional Ordinary Differential Equations.- Cauchy Problems for Fractional ODEs.- Boundary Value Problem for Fractional ODEs.- Part III: Time-Fractional Diffusion.- Subdiffusion: Hilbert Space Theory.- Subdiffusion: Hölder Space Theory.- Mathematical Preliminaries.- Index.
Klappentext
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.
The mathematical models are motivated by practical applications
Contains a complete mathematical theory of fractional differential equations
Suitable as a postgraduate-level textbook in applied and computational mathematics
Includes an up-to-date extensive list of references
Provides many examples and exercises
