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SpringerBriefs in Mathematics

Time-Fractional Differential Equations

A Theoretical Introduction

Authors: Kubica, Adam, Ryszewska, Katarzyna, Yamamoto, Masahiro

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  • Fills a gap found in existing monographs regarding feasible operator-theoretic foundations for wider applications 
  • Provides a background of time-fractional derivatives from the viewpoint of the operator theory in Sobolev spaces 
  • Justifies well-posedness for fractional differential equations in a self-contained manner
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eBook $44.99
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  • ISBN 978-981-15-9066-5
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  • Immediate eBook download after purchase
Softcover $59.99
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About this book

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.

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $44.99
price for Mexico
  • ISBN 978-981-15-9066-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for Mexico
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Bibliographic Information

Bibliographic Information
Book Title
Time-Fractional Differential Equations
Book Subtitle
A Theoretical Introduction
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2020
Publisher
Springer Singapore
Copyright Holder
The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-15-9066-5
DOI
10.1007/978-981-15-9066-5
Softcover ISBN
978-981-15-9065-8
Series ISSN
2191-8198
Edition Number
1
Number of Pages
X, 134
Number of Illustrations
4 b/w illustrations
Topics