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

• 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
• Physical Description: 1 online resource (VIII, 481 p.)

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.

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