Basic Theory
1st Edition
Published on 19. February 2019
VIII, 481 pages
978-3-11-057162-2 (ISBN)
Description
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.
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Anatoly Kochubei | Yuri Luchko
Basic Theory
Book
02/2024
1st Edition
De Gruyter
€189.95
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Anatoly Kochubei | Yuri Luchko
Basic Theory
E-Book
02/2019
1st Edition
De Gruyter
€189.95
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Persons
Anatoly N. Kochubei
, National Academy of Sciences, Ukraine;
Yuri Luchko
, Beuth University of Applied Sciences Berlin, Germany.
Content
- Intro
- 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
