Time-Fractional Differential Equations

A Theoretical Introduction

Adam Kubica, Katarzyna Ryszewska, Masahiro Yamamoto

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English

Springer Verlag, Singapore
30 November 2020

Series: SpringerBriefs in Mathematics

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.

By: Adam Kubica, Katarzyna Ryszewska, Masahiro Yamamoto
Imprint: Springer Verlag, Singapore
Country of Publication: Singapore
Edition: 1st ed. 2020
Dimensions: Height: 235mm, Width: 155mm,
Weight: 454g
ISBN: 9789811590658
ISBN 10: 9811590656
Series: SpringerBriefs in Mathematics
Pages: 134
Publication Date: 30 November 2020
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Reviews for Time-Fractional Differential Equations: A Theoretical Introduction

“The book is written nicely and useful as an introductory book on time fractional derivatives in abstract spaces.” (Syed Abbas, zbMATH 1485.34002, 2022)