December 2001 - 011202
Review Papers on Differential Equations of Fractional order by A. Kilbas and J. Trujillo

A.A. Kilbas and J.J. Trujillo, Differential equations of fractional order: methods, results and problems
- Part I (pp 39) Journal of Applicable Analysis vol 78 Nos. 1-2 (2001) 153-192.
- Part II (pp 49) ournal of Applicable Analysis, to appear

ABSTRACT part 1

The paper 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.
A survey of the methods and results in the theory of such ordinary fractional differential equations is given.
In particular, the method based on the reduction of the Cauchy-type problem for the fractional differential equations to the Volterra integral equations is discussed, and the Laplace transform, operational calculus and compositional methods for the solution of linear differential equations of fractional order are presented.
Problems and new trends of research are discussed.

AMS: 34A05, 34A25, 34A46, 26A33, 44A10, 45D05, 44A40, 33E20

ABSTRACT part 2

The paper, being a continuation of the first one, 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 treatment of numerical methods for ordinary and partial fractional differential equations.
Problems and new trends of research are discussed.

AMS: 34A05, 34A25, 34A46, 35A08, 35A22, 26A33, 44A10, 42B10, 65L05, 41A30, 33E20