Prabhakar function of Le Roy type: a set of results in the complex plane

Paneva-Konovska, Jordanka

doi:10.1007/s13540-022-00116-1

Cited by 8 publications

(15 citation statements)

References 28 publications

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“…• For m = 1 we have the E-K image of the Prabhakar type function F (γ) α;β; τ studied in Paneva-Konovska [25] and [26], namely:…”

Section: Some Particular Casesmentioning

confidence: 99%

“…The proof is omitted because of its simplicity, as a corollary of Th. 10 in [25] for the R-L integral. Similar results are provided in [25] for the R-L and E-K fractional derivatives.…”

Section: Some Particular Casesmentioning

confidence: 99%

“…10 in [25] for the R-L integral. Similar results are provided in [25] for the R-L and E-K fractional derivatives.…”

Section: Some Particular Casesmentioning

confidence: 99%

“…This can be called Le Roy function of Prabhakar type (with 4 indices, abbrev. MLPR), or Prabhakar function of Le Roy type, and is studied in details by Paneva-Konovska [25] and [26], also for extended conditions on the parameters:…”

Section: Introductionmentioning

confidence: 99%

“…Many properties of the functions (1.3), (1.5), (1.9), (1.7) are studied in details in the mentioned papers [25,18,32,26], see also [22,23] and [24]. For example, various type of integral representations of Mellin-Barnes-type are proposed (depending on the parameters), some inequalities and asymptotic formulae are obtained, and relations between Le Roy type functions with different number of parameters under some integrals and derivatives of integer or fractional orders.…”

Section: Introductionmentioning

confidence: 99%

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Erd\'{e}lyi-Kober Fractional Integrals (Part 2) of the Multi-Index Mittag-Leffler-Prabhakar Functions of Le Roy Type

Kiryakova,

Paneva-Konovska,

Rogosin

et al. 2023

Int. J. of Appl. Math.

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This is a continuation (Part 2) of our previous paper (Part 1), [28]. We study the multi-index generalizations (with 3m and 4m indices) of the classical Le Roy function and its Mittag-Leffler analogues, initiated recently by Gerhold, Garra and Polito and then studied by several other authors. In Part 1, along with the basic analytical properties, we provided the Laplace transform of the multi-index Le Roy type functions. Here, for these new special functions we consider the Erdélyi-Kober fractional order integral as one of the basic operators of Fractional Calculus (FC). The results are also specified for the particular cases of the Le Roy type functions as well as for the Riemann-Liouville and other specific cases of this operator. Finally, we propose another more general definition for the multi-index Le Roy functions and alternative interpretations, and mention about the possibilities to relate them with special functions more general than Fox H-function.

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“…• For m = 1 we have the E-K image of the Prabhakar type function F (γ) α;β; τ studied in Paneva-Konovska [25] and [26], namely:…”

Section: Some Particular Casesmentioning

confidence: 99%

“…The proof is omitted because of its simplicity, as a corollary of Th. 10 in [25] for the R-L integral. Similar results are provided in [25] for the R-L and E-K fractional derivatives.…”

Section: Some Particular Casesmentioning

confidence: 99%

“…10 in [25] for the R-L integral. Similar results are provided in [25] for the R-L and E-K fractional derivatives.…”

Section: Some Particular Casesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%