- eBook:Time-Fractional Differential Equations: A Theoretical Introduction
- Author:Adam Kubica, Katarzyna Ryszewska, Masahiro Yamamoto
- Edition:1st ed. 2020 edition
- Data:November 30, 2020
- Pages:144 pages
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.
2. Definition of Fractional Derivatives in Sobolev Spaces and Properties
3. Fractional Ordinary Differential Equations
4. Initial Boundary Value Problems for Time-Fractional Diffusion Equations
5. Decay Rate as t →∞
6. Concluding Remarks on Future Works
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