Fractional integrals and derivatives: theory and applications. Transl. from the Russian. (English) Zbl 0818.26003

Samko, St. G.; Kilbas, A. A.; Marichev, O. I.

New York, NY: Gordon and Breach. xxxvi, 976 p. (1993).

See the review of the Russian original (1987) in Zbl 0617.26004.

MSC:

26A33	Fractional derivatives and integrals
26-02	Research exposition (monographs, survey articles) pertaining to real functions
44A10	Laplace transform
35Q05	Euler-Poisson-Darboux equations
34B99	Boundary value problems for ordinary differential equations
44A15	Special integral transforms (Legendre, Hilbert, etc.)
45E10	Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
42A38	Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
45B05	Fredholm integral equations

Keywords:

integrals and derivatives of fractional order; integral transforms; Erdélyi-Kober operators; fractional integro-differentiation in Hadamard’s sense; fractional Weyl integrals; fractional integro- differentiation in M. Riesz’ sense; applications to differential equations and integral equations; Euler-Poisson-Darboux equations

Citations:

Zbl 0617.26004