Fractional Ordinary Differential Equations

First we consider simple fractional ordinary differential equations: $$\displaystyle \begin{aligned} D_t^{\alpha} u(t) = -\lambda u(t) + f(t), \quad 0

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Adam Kubica Katarzyna Ryszewska Masahiro Yamamoto

Time-Fractional Differential Equations A Theoretical Introduction


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Adam Kubica • Katarzyna Ryszewska • Masahiro Yamamoto

Time-Fractional Differential Equations A Theoretical Introduction

Adam Kubica Warsaw University of Technology Warszawa, Poland

Katarzyna Ryszewska Warsaw University of Technology Warszawa, Poland

Masahiro Yamamoto Graduate School of Mathematical Sciences The University of Tokyo Tokyo, Japan

ISSN 2191-8198 ISSN 2191-8201 (electronic) SpringerBriefs in Mathematics ISBN 978-981-15-9065-8 ISBN 978-981-15-9066-5 (eBook) Mathematics Subject Classification: 35R11, 26A33 © The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by