Kilbas, A. A.; Trujillo, J. J. Differential equations of fractional order: Methods, results and problems. II. (English) Zbl 1033.34007 Appl. Anal. 81, No. 2, 435-493 (2002). 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. Cited in 1 ReviewCited in 132 Documents 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 Keywords:differential equations of fractional order; partial fractional differential equations Citations:Zbl 1031.34002 PDFBibTeX XMLCite \textit{A. A. Kilbas} and \textit{J. J. Trujillo}, Appl. Anal. 81, No. 2, 435--493 (2002; Zbl 1033.34007) Full Text: DOI