Volume 2 Fractional Differential Equations

Book

Volume 2 Fractional Differential Equations

Edited by: Anatoly Kochubei and Yuri Luchko

Part of the multi-volume work

Handbook of Fractional Calculus with Applications

Language: English

Published/Copyright: 2019

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De Gruyter Reference

About this book

This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.

A unique, comprehensive overview of fractional calculus and its applications
With authoritative contributions from the world's leading experts
Of interest to mathematicians, physicists, and engineers

Author / Editor information

Anatoly N. Kochubei, National Academy of Sciences, Ukraine; Yuri Luchko, Beuth University of Applied Sciences Berlin, Germany.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	V
Contents Publicly Available Download PDF	VII
General theory of Caputo-type fractional differential equations Kai Diethelm Requires Authentication Unlicensed Licensed	1
Problems of Sturm–Liouville type for differential equations with fractional derivatives Temirkhan Aleroev and Hedi Aleroeva Requires Authentication Unlicensed Licensed	21
Maps with power-law memory: direct introduction and Eulerian numbers, fractional maps, and fractional difference maps Mark Edelman Requires Authentication Unlicensed Licensed	47
Symmetries and group invariant solutions of fractional ordinary differential equations Rafail K. Gazizov, Alexey A. Kasatkin and Stanislav Yu. Lukashchuk Requires Authentication Unlicensed Licensed	65
Operational method for fractional ordinary differential equations Yuri Luchko Requires Authentication Unlicensed Licensed	91
Lyapunov-type inequalities for fractional boundary value problems Mohamed Jleli, Mokhtar Kirane and Bessem Samet Requires Authentication Unlicensed Licensed	119
Fractional-parabolic equations and systems. Cauchy problem Anatoly N. Kochubei Requires Authentication Unlicensed Licensed	145
Time fractional diffusion equations: solution concepts, regularity, and long-time behavior Rico Zacher Requires Authentication Unlicensed Licensed	159
Layer potentials for the time-fractional diffusion equation Jukka Kemppainen Requires Authentication Unlicensed Licensed	181
Fractional-hyperbolic equations and systems. Cauchy problem Anatoly N. Kochubei Requires Authentication Unlicensed Licensed	197
Equations with general fractional time derivatives–Cauchy problem Anatoly N. Kochubei Requires Authentication Unlicensed Licensed	223
User’s guide to the fractional Laplacian and the method of semigroups Pablo Raúl Stinga Requires Authentication Unlicensed Licensed	235
Parametrix methods for equations with fractional Laplacians Victoria P. Knopova, Anatoly N. Kochubei and Alexei M. Kulik Requires Authentication Unlicensed Licensed	267
Maximum principle for the time-fractional PDEs Yuri Luchko and Masahiro Yamamoto Requires Authentication Unlicensed Licensed	299
Wave equation involving fractional derivatives of real and complex fractional order Teodor M. Atanacković, Sanja Konjik and Stevan Pilipović Requires Authentication Unlicensed Licensed	327
Symmetries, conservation laws and group invariant solutions of fractional PDEs Rafail K. Gazizov, Alexey A. Kasatkin and Stanislav Yu. Lukashchuk Requires Authentication Unlicensed Licensed	353
Fractional Duhamel principle Sabir Umarov Requires Authentication Unlicensed Licensed	383
Inverse problems of determining sources of the fractional partial differential equations Yikan Liu, Zhiyuan Li and Masahiro Yamamoto Requires Authentication Unlicensed Licensed	411
Inverse problems of determining parameters of the fractional partial differential equations Zhiyuan Li, Yikan Liu and Masahiro Yamamoto Requires Authentication Unlicensed Licensed	431
Inverse problems of determining coefficients of the fractional partial differential equations Zhiyuan Li and Masahiro Yamamoto Requires Authentication Unlicensed Licensed	443
Abstract linear fractional evolution equations Carlos Lizama Requires Authentication Unlicensed Licensed	465
Abstract nonlinear fractional evolution equations Carlos Lizama Requires Authentication Unlicensed Licensed	499
Index Requires Authentication Unlicensed Licensed	515

Publishing information

Pages and Images/Illustrations in book

eBook published on:

February 19, 2019

eBook ISBN:

9783110571660

Hardcover published on:

February 19, 2019

Hardcover ISBN:

9783110570823

Pages and Images/Illustrations in book

Front matter:

8

Main content:

519

Illustrations:

2

Coloured Illustrations:

2

Tables:

15

https://doi.org/10.1515/9783110571660

eBook ISBN: 9783110571660

Hardcover ISBN: 9783110570823

Keywords for this book

Gebrochene Analysis

Audience(s) for this book

Researchers and graduate students in mathematics, physics, and engineering.

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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com

Volume 2 Fractional Differential Equations

Overview

About this book

Author / Editor information

Topics

Table of contents

Bibliographic data