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.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

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 
@article{FCAA_2008_11_2_a5,
     author = {Kiryakova, Virginia},
     title = {A {Brief} {Story} about the {Operators} of the {Generalized} {Fractional} {Calculus}},
     journal = {Fractional calculus and applied analysis},
     pages = {203--220},
     publisher = {mathdoc},
     volume = {11},
     number = {2},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/FCAA_2008_11_2_a5/}
}
TY  - JOUR
AU  - Kiryakova, Virginia
TI  - A Brief Story about the Operators of the Generalized Fractional Calculus
JO  - Fractional calculus and applied analysis
PY  - 2008
SP  - 203
EP  - 220
VL  - 11
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FCAA_2008_11_2_a5/
LA  - en
ID  - FCAA_2008_11_2_a5
ER  - 
%0 Journal Article
%A Kiryakova, Virginia
%T A Brief Story about the Operators of the Generalized Fractional Calculus
%J Fractional calculus and applied analysis
%D 2008
%P 203-220
%V 11
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FCAA_2008_11_2_a5/
%G en
%F FCAA_2008_11_2_a5
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/