Derivatives, unnatural-order integrals, and a class of linear differential equations with unnatural derivatives (Q1780236)

The first four pages of the paper contain some known properties of fractional integrals and derivatives from the well-known sources. The remaining 5 pages contain successive approximations to a solution of a special class of linear fractional differential equations with constant coefficients (LFSECC). For the solution given as a limit of successive approximations no proof of convergence is given. Reviewer's remark. There exists a vast bibliography on fractional differential equations not cited in the paper. We refer for example to the book by \textit{K. S. Miller} and \textit{B. Ross} [An introduction to the fractional calculus and fractional differential equations. New York: John Wiley \& Sons, Inc. (1993; Zbl 0789.26002)], and to the survey papers [\textit{A. A. Kilbas} and \textit{J. J. Trujillo}, Appl. Anal. 78, No. 1--2, 153--192 (2001; Zbl 1031.34002), Appl. Anal. 81, No. 2, 435--493 (2002; Zbl 1033.34007) and \textit{A. A. Kilbas, H. M. Srivastava} and \textit{J. J. Trujillo}, in: Stefan Samko (ed.) et al., Factorization, singular operators and related problems. Proceedings of the conference in honor of Professor Georgii Litvinchuk, Funchal, Madeira, Portugal, January 28--February 1, 2002. Doredrecht: Kluwer Academic Publishers. 151--173 (2003; Zbl 1053.35038)] on such equations, where many other references may be found. The book above, in particular, deals with LFSECC.