Abstract
The aim of this work is to describe main aspects of the modern theory of fractional differential equations, to present elements of classification of fractional differential equations, to formulate basic components of investigations related to fractional differential equations, to pose some open problems in the study of fractional differential equations. A survey of results by S.G. Samko on different problems of modern mathematical analysis is given. Main results of S.G. Samko having an essential influence on the establishing and development of the theory of fractional differential equations are singled out.
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