Geodesic
A Brief Story about the Operators of the Generalized Fractional Calculus
Fractional calculus and applied analysis, Tome 11 (2008) no. 2, pp. 203-220

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In this survey we present a brief history and the basic ideas of the generalized fractional calculus (GFC). The notion “generalized operator of fractional integration” appeared in the papers of the jubilarian Prof. S.L. Kalla in the years 1969-1979 when he suggested the general form of these operators and studied examples of them whose kernels were special functions as the Gauss and generalized hypergeometric functions, including arbitrary G- and H-functions. His ideas provoked the author to choose a more peculiar case of such kernels and to develop a theory of the corresponding GFC that featured many applications. All known fractional integrals and derivatives and other generalized integration and differential operators in various areas of analysis happened to fall in the scheme of this GFC.
Keywords: Fractional Calculus, Generalized Fractional Integrals and Derivatives, Generalized Hypergeometric Functions, 26A33, 33C60, 44A20 
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Kiryakova, Virginia. A Brief Story about the Operators of the Generalized Fractional Calculus. Fractional calculus and applied analysis, Tome 11 (2008) no. 2, pp. 203-220. http://geodesic.mathdoc.fr/item/FCAA_2008_11_2_a5/