Handbook of Fractional Calculus with Applications.

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

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, integ...

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Bibliographic Details
Superior document:Title is part of eBook package: De Gruyter DG Plus eBook-Package 2019
MitwirkendeR:
Almeida, Ricardo,
Atanacković, Teodor M.,
Gorenflo, Rudolf,
Hilfer, Rudolf,
Kiryakova, Virginia,
Kochubei, Anatoly N.,
Konjik, Sanja,
Kwaśnicki, Mateusz,
Luchko, Yuri,
Mainardi, Francesco,
Malamud, Mark M.,
Meerschaert, Mark M.,
Meerschaert, Mark,
Nane, Erkan,
Paris, Richard B.,
Pilipović, Stevan,
Rogosin, Sergei,
Scheffler, Hans Peter,
Sidi Ammi, Moulay Rchid,
Tenreiro Machado, J. A.,
Torres, Delfim F. M.,
Vellaisamy, P.,
HerausgeberIn:
Kochubei, Anatoly,
Luchko, Yuri,
Place / Publishing House:Berlin ;, Boston : : De Gruyter, , [2019]
©2019
Year of Publication:2019
Language:English
Series:De Gruyter Reference ; Volume 1
Online Access:
Physical Description:1 online resource (VIII, 481 p.)
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Table of 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

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