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Zbl 1033.34007
Kilbas, A. A.; Trujillo, J. J.
Differential equations of fractional order: Methods, results and problems. II. (English)
[J] Appl. Anal. 81, No. 2, 435-493 (2002). ISSN 0003-6811; ISSN 1563-504X/e

Summary: The article, being a continuation of the first one [ibid. 78, 153--192 (2001; Zbl 1031.34002)], deals with the so-called differential equations of fractional order in which an unknown function is contained under the operation of a derivative of fractional order. The methods and the results in the theory of such fractional differential equations are presented including the Dirichlet-type problem for ordinary fractional differential equations, studying such equations in spaces of generalized functions, partial fractional differential equations and more general abstract equations, and a treatment of numerical methods for ordinary and partial fractional differential equations. Problems and new trends of research are discussed.

MSC 2000:: *34A25 Analytical theory of ODE
26A33 Fractional derivatives and integrals (real functions)
33E20 Functions defined by series and integrals
35A22 Transform methods (PDE)
44A10 Laplace transform
65L99 Numerical methods for ODE
65M99 Numerical methods for IVP of PDE

Keywords: differential equations of fractional order; partial fractional differential equations

Citations: Zbl 1031.34002

Cited in: Zbl 1096.34004

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