Luchko, Yury Operational rules for a mixed operator of the Erdélyi-Kober type. (English) Zbl 1128.26004 Fract. Calc. Appl. Anal. 7, No. 3, 339-364 (2004). 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)]. Reviewer: J. M. C. Joshi (Uttaranchal) Cited in 12 Documents MSC: 26A33 Fractional derivatives and integrals 44A40 Calculus of Mikusiński and other operational calculi 44A35 Convolution as an integral transform 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 PDFBibTeX XMLCite \textit{Y. Luchko}, Fract. Calc. Appl. Anal. 7, No. 3, 339--364 (2004; Zbl 1128.26004) Full Text: EuDML