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Differential equations of fractional order: Methods, results and problems. II. (English) Zbl 1033.34007

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:

34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
26A33 Fractional derivatives and integrals
33E20 Other functions defined by series and integrals
35A22 Transform methods (e.g., integral transforms) applied to PDEs
44A10 Laplace transform
65L99 Numerical methods for ordinary differential equations
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems

Citations:

Zbl 1031.34002
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