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 |