Volume 2 Fractional Differential Equations

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Volume 2 Fractional Differential Equations

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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

Publicly Available

Frontmatter
I

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Preface
V

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Contents
VII

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General theory of Caputo-type fractional differential equations
1
Kai Diethelm

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Problems of Sturm–Liouville type for differential equations with fractional derivatives
21
Temirkhan Aleroev and Hedi Aleroeva

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Maps with power-law memory: direct introduction and Eulerian numbers, fractional maps, and fractional difference maps
47
Mark Edelman

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Symmetries and group invariant solutions of fractional ordinary differential equations
65
Rafail K. Gazizov, Alexey A. Kasatkin and Stanislav Yu. Lukashchuk

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Operational method for fractional ordinary differential equations
91
Yuri Luchko

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Lyapunov-type inequalities for fractional boundary value problems
119
Mohamed Jleli, Mokhtar Kirane and Bessem Samet

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Fractional-parabolic equations and systems. Cauchy problem
145
Anatoly N. Kochubei

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Time fractional diffusion equations: solution concepts, regularity, and long-time behavior
159
Rico Zacher

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Layer potentials for the time-fractional diffusion equation
181
Jukka Kemppainen

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Fractional-hyperbolic equations and systems. Cauchy problem
197
Anatoly N. Kochubei

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Equations with general fractional time derivatives–Cauchy problem
223
Anatoly N. Kochubei

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User’s guide to the fractional Laplacian and the method of semigroups
235
Pablo Raúl Stinga

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Parametrix methods for equations with fractional Laplacians
267
Victoria P. Knopova, Anatoly N. Kochubei and Alexei M. Kulik

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Maximum principle for the time-fractional PDEs
299
Yuri Luchko and Masahiro Yamamoto

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Wave equation involving fractional derivatives of real and complex fractional order
327
Teodor M. Atanacković, Sanja Konjik and Stevan Pilipović

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Symmetries, conservation laws and group invariant solutions of fractional PDEs
353
Rafail K. Gazizov, Alexey A. Kasatkin and Stanislav Yu. Lukashchuk

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Fractional Duhamel principle
383
Sabir Umarov

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Inverse problems of determining sources of the fractional partial differential equations
411
Yikan Liu, Zhiyuan Li and Masahiro Yamamoto

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Inverse problems of determining parameters of the fractional partial differential equations
431
Zhiyuan Li, Yikan Liu and Masahiro Yamamoto

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Inverse problems of determining coefficients of the fractional partial differential equations
443
Zhiyuan Li and Masahiro Yamamoto

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Abstract linear fractional evolution equations
465
Carlos Lizama

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Abstract nonlinear fractional evolution equations
499
Carlos Lizama

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Index
515

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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

Frontmatter

Preface

Contents

General theory of Caputo-type fractional differential equations

Problems of Sturm–Liouville type for differential equations with fractional derivatives

Maps with power-law memory: direct introduction and Eulerian numbers, fractional maps, and fractional difference maps

Symmetries and group invariant solutions of fractional ordinary differential equations

Operational method for fractional ordinary differential equations

Lyapunov-type inequalities for fractional boundary value problems

Fractional-parabolic equations and systems. Cauchy problem

Time fractional diffusion equations: solution concepts, regularity, and long-time behavior

Layer potentials for the time-fractional diffusion equation

Fractional-hyperbolic equations and systems. Cauchy problem

Equations with general fractional time derivatives–Cauchy problem

User’s guide to the fractional Laplacian and the method of semigroups

Parametrix methods for equations with fractional Laplacians

Maximum principle for the time-fractional PDEs

Wave equation involving fractional derivatives of real and complex fractional order

Symmetries, conservation laws and group invariant solutions of fractional PDEs

Fractional Duhamel principle

Inverse problems of determining sources of the fractional partial differential equations

Inverse problems of determining parameters of the fractional partial differential equations

Inverse problems of determining coefficients of the fractional partial differential equations

Abstract linear fractional evolution equations

Abstract nonlinear fractional evolution equations

Index

Bibliographic data