Handbook of Fractional Calculus with Applications. Volume 2, Fractional Differential Equations / Anatoly Kochubei, Yuri Luchko.

Format:

Book

Contributor:

Kochubei, Anatoly, Editor.

Luchko, Yuri, Editor.

Series:

De Gruyter reference ; Volume 2.

De Gruyter Reference ; Volume 2

Language:

English

Subjects (All):

Fractional calculus.

Physical Description:

1 online resource (527 pages) : illustrations.

Place of Publication:

Berlin ; Boston : De Gruyter, [2019]

Language Note:

In English.

Summary:

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.

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

Notes:

Description based on online resource; title from PDF title page (publisher's Web site, viewed 06. Apr 2020)

ISBN:

9783110571059

3110571056

9783110571660

3110571668

OCLC:

1091703164