Handbook of Fractional Calculus with Applications. Volume 1, Basic Theory

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