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On the generalized Mittag-Leffler function and its application in a fractional telegraph equation. (English) Zbl 1245.33020
Summary: The classical Mittag-Leffler functions, involving one- and two-parameter, play an important role in the study of fractional-order differential (and integral) equations. The so-called generalized Mittag-Leffler function, a function with three-parameter which generalizes the classical ones, appear in the fractional telegraph equation. Here we introduce some integral transforms associated with this generalized Mittag-Leffler function. As particular cases some recent results are recovered.
##### MSC:
 33E12 Mittag-Leffler functions and generalizations 26A33 Fractional derivatives and integrals (real functions)