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. 12
(2001) 153192.
 Part II (pp 49) ournal of Applicable Analysis, to appear
ABSTRACT part 1
The paper deals with the socalled 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 Cauchytype
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 socalled 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 Dirichlettype 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
