Handbook of Fractional Calculus with Applications. Volume 1, Basic Theory / Anatoly Kochubei, Yuri Luchko.

Format:

Book

Contributor:

Kochubei, Anatoly, Editor.

Luchko, Yuri, Editor.

Series:

De Gruyter reference.

De Gruyter Reference ; Volume 1

Language:

English

Subjects (All):

Fractional calculus.

Physical Description:

1 online resource (490 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 first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.

Contents:

Frontmatter

Preface

Contents

Recent history of the fractional calculus: data and statistics

Basic FC operators and their properties

Mathematical and physical interpretations of fractional derivatives and integrals

Generalized fractional calculus operators with special functions

General fractional calculus

Multiple Erdélyi-Kober integrals and derivatives as operators of generalized fractional calculus

Fractional Laplace operator and its properties

Applications of the Mellin integral transform technique in fractional calculus

Fractional Fourier transform

The Wright function and its applications

Mittag-Leffler function: properties and applications

Asymptotics of the special functions of fractional calculus

Analysis of fractional integro-differential equations of thermistor type

A survey on fractional variational calculus

Variational principles with fractional derivatives

Continuous time random walks and space-time fractional differential equations

Inverse subordinators and time fractional equations

Spectral theory of fractional order integration operators, their direct sums, and similarity problem to these operators of their weak perturbations

Fractional differentiation in p-adic analysis

Index

Notes:

Includes bibliographical references and index.

Description based on: online resource; title from pdf title page (de Gruyter, viewed on March 14, 2023).

ISBN:

3-11-057162-5

3-11-057063-7

OCLC:

1091666315