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Paneva-Konovska, Jordanka

Overconvergence of series in generalized Mittag-Leffler functions. (English) Zbl 1364.33020

Fract. Calc. Appl. Anal. 20, No. 2, 506-520 (2017).
Summary: Series defined by means of the three-parametric Mittag-Leffler functions, called also the Prabhakar functions, are considered in this paper. Their behaviour is investigated on the boundaries of the convergence domains. Necessary and sufficient conditions for their overconvergence are proposed. The corresponding results for series in Mittag-Leffler functions are discussed as a particular case. Such kind of results are motivated by the fact that the solutions of some fractional order differential and integral equations can be written in terms of series (or series of integrals) of Mittag-Leffler type functions.

Cited in 6 Documents

MSC:

33E12 Mittag-Leffler functions and generalizations
40A30 Convergence and divergence of series and sequences of functions
30B30 Boundary behavior of power series in one complex variable; over-convergence
30B10 Power series (including lacunary series) in one complex variable

Keywords:

Mittag-Leffler functions and generalizations; series in generalized Mittag-Leffler functions; overconvergence; Hadamard gaps
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References:

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