A Multi-Index Borel-Dzrbashjan Transform
F. Al-Musallam, V. Kiryakova, and V. Kim Tuan
Source: Rocky Mountain J. Math. Volume 32, Number 2
(2002), 409-429.
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Keywords: Laplace-type integral transform; Mittag-Leffler function; $H$-transform; operators of fractional integration and differentiation; BorelDzrbashian transform
Full-text: Open access
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Permanent link to this document: http://projecteuclid.org/euclid.rmjm/1181070079
Digital Object Identifier: doi:10.1216/rmjm/1030539678
Mathematical Reviews number (MathSciNet): MR1934897
Zentralblatt MATH identifier: 1035.44002
References
I. Dimovski, Operational calculus for a differential operator, C.R. Acad. Bulg. Sci. 19 (1966), 1111-1114.
Mathematical Reviews (MathSciNet): MR205001
--------, On a Bessel-type integral transformation due to N. Obrechkoff, C.R. Acad. Bulg. Sci. 27 (1966), 23-26.
Zentralblatt MATH: 0325.44003
Mathematical Reviews (MathSciNet): MR333620
I. Dimovski and V. Kiryakova, Convolution and differential property of the Borel-Dzrbashjan transform, in Proceedings of Complex Analysis and Applications, Varna 1981, Publ. House BAS, Sofia, 1984.
--------, The Obrechkoff integral transform: Properties and relation to generalized fractional calculus, Numer. Functional Anal. Optim. 21 (2000), 121-144.
Mathematical Reviews (MathSciNet): MR1759992
Digital Object Identifier: doi:10.1080/01630560008816944
M.M. Dzrbashjan, Integral transforms and representations of functions in the complex domain, Nauka, Moscow, 1966.
Mathematical Reviews (MathSciNet): MR209472
A. Erdélyi et al., Higher transcendental functions, McGraw-Hill, New York, 1953.
I.I. Hirshman and D.V. Widder, The convolutional transforms, Princeton University Press, Princeton, 1955.
V. Kiryakova, Generalized fractional calculus and applications, Longman, Harlow & J. Wiley Ltd., New York, 1994.
Mathematical Reviews (MathSciNet): MR1265940
Zentralblatt MATH: 0882.26003
--------, Multiple (multi-index) Mittag-Leffler functions and relations to generalized fractional calculus, J. Comput. Appl. Math. 118 (2000), 241-259.
Mathematical Reviews (MathSciNet): MR1765953
Zentralblatt MATH: 0966.33011
Digital Object Identifier: doi:10.1016/S0377-0427(00)00292-2
A.M. Mathai and R.K. Saxena, The $H$-function with applications in statistics and other disciplines, Wiley Eastern Ltd., New Delhi, 1978.
Mathematical Reviews (MathSciNet): MR513025
Zentralblatt MATH: 0382.33001
N. Obrechkoff, On some integral representations of real functions on the real half-line, Izvestija Mat. Inst. (Sofia) 1 (1958), 3-33.
Mathematical Reviews (MathSciNet): MR1446173
A.A. Prudnikov, Yu.A. Brychkov and O.I. Marichev, Integrals and series. More special functions, Gordon & Breach Sci. Publ., New York, 1990.
Mathematical Reviews (MathSciNet): MR1054647
Zentralblatt MATH: 1103.33300
S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional integrals and derivatives. Theory and applications, Gordon & Breach Sci. Publ., New York, 1993.
Mathematical Reviews (MathSciNet): MR1347689
H.M. Srivastava, K.C. Gupta and S.P. Goyal, The $H$-functions of one and two variables with applications, South Asian Publ., New Delhi, 1982.
Mathematical Reviews (MathSciNet): MR691138
Zentralblatt MATH: 0506.33007
E.C. Titchmarsh, Introduction to the theory of Fourier integrals, Clarendon Press, Oxford, 1937.
Vu Kim Tuan, On the factorization of convolution type integral transforms in the space $L^\Phi_2$, Dokl. Acad. Nauk Armyanskov 83 (1986), 7-10 (in Russian).
Mathematical Reviews (MathSciNet): MR888633
--------, Integral transforms and their compositional structure, Dr.Sc. thesis, Belarussian State Univ., Minsk, 1987 (in Russian).
Rocky Mountain Journal of Mathematics