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Operational rules for a mixed operator of the Erdélyi-Kober type. (English) Zbl 1128.26004
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 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)].
26A33Fractional derivatives and integrals (real functions)
44A40Calculus of Mikusiński and other operational calculi
44A35Convolution (integral transforms)