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Zbl 1128.26004
Luchko, Yury
Operational rules for a mixed operator of the Erdélyi-Kober type. (English)
[J] Fract. Calc. Appl. Anal. 7, No. 3, 339-364 (2004). ISSN 1311-0454; ISSN 1314-2224/e

This research paper, which has been dedicated to Professor Ivan H. Dimnovski on his 70th birthday, considers a mixed operator of Erdelyi-Kober type. It has been shown how the Mellin transform technique can be used to construct different representations of this operator. For special cases of parameters the operator is reduced to some well known differential, integro-differential, or integral operators already studied. See also {\it J. M. C. Joshi} [Ranchi Univ. Math. J. 24 (1993), 53--68 (1993; Zbl 1023.46044) and Integral Transforms Spec. Funct. 15, No. 2, 117--127 (2004; Zbl 1063.44004)].
[J. M. C. Joshi (Uttaranchal)]

MSC 2000:: *26A33 Fractional derivatives and integrals (real functions)
44A40 Calculus of Mikusinski, etc.
44A35 Convolution

Keywords: operational relations; fractional derivatives; fractional integrals; special functions; Mikusinski type operational calculus; Riemann-Liouville fractional integral operator

Citations: Zbl 1023.46044; Zbl 1063.44004

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