Geodesic
On two special functions, generalizing the~Mittag-Leffler type function, their~properties~and~applications
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2012), pp. 52-65

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Two special functions, concerning Mittag-Leffler type functions, are studied. The first is the modification of generalized Mittag–Leffler function, which was introduced by A. A. Kilbas and M. Saigo; the second is the special case of the first one. The relation of these functions with some elementary and special functions and their role in solving of Abel–Volterra integral equations is indicated. The formulas of the fractional integration and differentiation in sense of Riemann–Liouville and Kober are presented. The applications to Cauchy type problems for some linear fractional differential equations with Riemann-Liouville and Kober derivatives are noticed.
Keywords: special functions, Mittag–Leffler type function, Riemann–Liouville integral and differential operators, fractional differential and integral equations, Cauchy type problems. 
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     title = {On two special functions, generalizing {the~Mittag-Leffler} type function, their~properties~and~applications},
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E. N. Ogorodnikov. On two special functions, generalizing the~Mittag-Leffler type function, their~properties~and~applications. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2012), pp. 52-65. http://geodesic.mathdoc.fr/item/VSGTU_2012_1_a5/