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Riemann-Liouville Fractional Calculus and Multiindex Dzrbashjan-Gelfond-Leontiev Differentiation and Integration with Multiindex Mittag-Leffler Function

Authors: U.K. Saha, L.K. Arora

Abstract:

The multiindex Mittag-Leffler (M-L) function and the multiindex Dzrbashjan-Gelfond-Leontiev (D-G-L) differentiation and integration play a very pivotal role in the theory and applications of generalized fractional calculus. The object of this paper is to investigate the relations that exist between the Riemann-Liouville fractional calculus and multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration with multiindex Mittag-Leffler function.

Keywords: Multiindex Mittag-Leffler function, Multiindex Dzrbashjan-Gelfond-Leontiev differentiation and integration, Riemann-Liouville fractional integrals and derivatives.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1335366

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[1] I. Dimovski, V. Kiryakova, Convolution and Commutant of Gelfond- Leontiev Operator of Integration, Proceedings of the Constructive Function Theory, Varna- 1981, Publ. House BAS, Sofia, 1983, 288-294.
[2] I. Dimovski, V. Kiryakova, Convolution and Differential Property of the Borel-Dzrbashjan Transform, in: Proceedings of the Complex Analysis and Applications, Varna- 1981, Publ. House BAS, Sofia, 1984, 148-156.
[3] M.M. Dzrbashjan, On the Integral Transformation Generated by the Generalized Mittag-Leffler function (in Russian), Izv. AN Arm. SSR 13(3) (1960), 21-63.
[4] A. Erdelyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Higher Transcendental Functions,Vol. III, NewYork, Toronto, London: McGraw-Hill Book Company, 1955.
[5] V. Kiryakova, The Multi-index Mittag-Leffler Functions as an Important Class of Special Functions of Fractional Calculus, Computers and Math. With Appl. 59 (5) (2010), 1885-1895.
[6] V. Kiryakova, Multiindex Mittag-Leffler Functions, Related Gelfond- Leontiev Operators and Laplace Type Integral Transforms, Fract. Calc. Appl. Anal. 2 (4) (1999), 445-462.
[7] V. Kiryakova, Multiple (multiindex) Mittag-Leffler Functions and Relations to Generalized Fractional Calculus, J. Comput. Appl. Math. 118 (2000), 241-259.
[8] V. Kiryakova, Generalized Fractional Calculus and Applications, Research Notes in Math. Series, Vol. 301, NewYork: Pritam Longman, Harlow and Wiley, 1994.
[9] S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers, Reading, PA, 1993.