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Time-Fractional Differential Equations = A Theoretical Introduction /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Time-Fractional Differential Equations/ by Adam Kubica, Katarzyna Ryszewska, Masahiro Yamamoto.
其他題名:	A Theoretical Introduction /
作者:	Kubica, Adam.
其他作者:	Ryszewska, Katarzyna.
面頁冊數:	X, 134 p. 4 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Partial differential equations. -
電子資源:	https://doi.org/10.1007/978-981-15-9066-5
ISBN:	9789811590665

Time-Fractional Differential Equations = A Theoretical Introduction /
Kubica, Adam.

Time-Fractional Differential EquationsA Theoretical Introduction /[electronic resource] :by Adam Kubica, Katarzyna Ryszewska, Masahiro Yamamoto. - 1st ed. 2020. - X, 134 p. 4 illus.online resource. - SpringerBriefs in Mathematics,2191-8198. - SpringerBriefs in Mathematics,.

Chapter 1: Basics on fractional differentiation and integration -- Chapter 2: Definition of fractional derivatives in Sobolev spaces and properties -- Chapter 3: Fractional ordinary differential equations -- Chapter 4: Initial boundary value problems for time-fractional diffusion equations -- Chapter 5: Decay rate as t →∞ -- Chapter 6: Concluding remarks on future works.

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. <the fractional="" partial="" differential="" equations="" govern="" phenomena="" depending="" both="" on="" spatial="" and="" time="" variables="" require="" more="" subtle="" treatments.="" moreover,="" are="" highly="" demanded="" model="" for="" solving="" real-world="" problems="" such="" as="" the="" anomalous="" diffusion="" in="" heterogeneous="" media.

ISBN: 9789811590665

Standard No.: 10.1007/978-981-15-9066-5doiSubjects--Topical Terms:

1102982
Partial differential equations.

LC Class. No.: QA370-380

Dewey Class. No.: 515.353

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