Handbook of fractional calculus with applications. Volume 1, Basic theory /

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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Detalles Bibliográficos
Clasificación:Libro Electrónico
Otros Autores: Kochubei, Anatoly N. (Editor ), Luchko, Yurii F. (Editor )
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin ; Boston : De Gruyter, [2019]
Colección:De Gruyter reference.
Temas:
Fractional calculus.
Dérivées fractionnaires.
MATHEMATICS > Mathematical Analysis.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Frontmatter
  • Preface
  • Contents
  • Recent history of the fractional calculus: data and statistics / Tenreiro Machado, J.A. / Kiryakova, Virginia
  • Basic FC operators and their properties / Kochubei, Anatoly N. / Luchko, Yuri
  • Mathematical and physical interpretations of fractional derivatives and integrals / Hilfer, Rudolf
  • Generalized fractional calculus operators with special functions / Kiryakova, Virginia
  • General fractional calculus / Kochubei, Anatoly N.
  • Multiple Erdélyi-Kober integrals and derivatives as operators of generalized fractional calculus / Kiryakova, Virginia / Luchko, Yuri
  • Fractional Laplace operator and its properties / Kwaśnicki, Mateusz
  • Applications of the Mellin integral transform technique in fractional calculus / Luchko, Yuri / Kiryakova, Virginia
  • Fractional Fourier transform / Luchko, Yuri
  • The Wright function and its applications / Luchko, Yuri
  • Mittag-Leffler function: properties and applications / Gorenflo, Rudolf / Mainardi, Francesco / Rogosin, Sergei
  • Asymptotics of the special functions of fractional calculus / Paris, Richard B.
  • Analysis of fractional integro-differential equations of thermistor type / Sidi Ammi, Moulay Rchid / Torres, Delfim F.M.
  • A survey on fractional variational calculus / Almeida, Ricardo / Torres, Delfim F.M.
  • Variational principles with fractional derivatives / Atanacković, Teodor M. / Konjik, Sanja / Pilipović, Stevan
  • Continuous time random walks and space-time fractional differential equations / Meerschaert, Mark / Scheffler, Hans Peter
  • Inverse subordinators and time fractional equations / Meerschaert, Mark M. / Nane, Erkan / Vellaisamy, P.
  • Spectral theory of fractional order integration operators, their direct sums, and similarity problem to these operators of their weak perturbations / Malamud, Mark M.
  • Fractional differentiation in p-adic analysis / Kochubei, Anatoly N.
  • Index

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