This monograph delves into the theory of time-fractional diffusion and wave equations, presenting a comprehensive exploration of recent advancements in the field. Key topics include well-posedness, regularity, and approximate controllability of Cauchy problems, as well as the existence and regularity of terminal value problems. Detailed examples illustrate the applications of these equations, demonstrating their practical relevance. The content is rooted in research conducted by the author and other experts over the past five years, offering a thorough foundation for further study. This work is an invaluable resource for researchers, graduate students, and PhD candidates in the fields of differential equations, applied analysis, and related areas.
Preface.- Introduction.- Preliminaries.- Well-posedness of Fractional
Diffusion Equations.- Inverse Problems of Fractional Diffusion
Equations.- Well-posedness and Regularity of Fractional Wave
Equations.- Inverse Problems of Fractional Wave Equations.- References.-
Index.
Dr. Yong Zhou is a Professor at Macau University of Science and Technology. His research fields include fractional differential equations, evolution equations and control theory. Zhou has published seven monographs in Springer, Elsevier, De Gruyter, World Scientific respectively, and more than three hundred research papers in international journals including Mathematische Annalen, Journal of Functional Analysis, Nonlinearity, Inverse Problems, Proceedings of the Royal Society of Edinburgh, and so on. Zhou has undertaken five projects from National Natural Science Foundation of China, and two projects from the Macau Science and Technology Development Fund. He won the second prize of Chinese University Natural Science Award in 2000, and the second prize of Natural Science Award of Hunan Province, China in 2017 and 2021. Zhou had worked as an Associate Editor for IEEE Transactions on Fuzzy Systems, Journal of Applied Mathematics & Computing, Mathematical Inequalities & Applications, and an Editorial Board Member of Fractional Calculus and Applied Analysis.
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