Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus

By Virginia S. Kiryakova. 2000

216 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/06024c752b3a9db2cd40208c57c84eebcd94551e

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In Applied Mathematics

In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

Solving nonlinear fractional partial differential equations using the homotopy analysis method (2010, background): “Some fundamental works on various aspects of the fractional calculus are given by Abbasbandy [6], Caputo [7], Debanth [8], Diethelm et al. [9], Hayat et al. [10], Jafari and Seifi [11] [12], Kemple and Beyer [13], Kilbas and Trujillo [14], Kiryakova [15], Miller and Ross [2], Momani and Shawagfeh [1”
A Note on Fractional Integral Operator Associated with Multiindex Mittag-Leffler Functions (2016, background): “The theory of this class of functions has been developed in a series of articles by Kiryakova et al. [12–14, 16, 17] (see also [8] and [24]).”
A BRIEF STORY ABOUT THE OPERATORS OF THE GENERALIZED FRACTIONAL CALCULUS (2008, methodology): “Some of them can be seen in the monograph [17] and articles [18, 20, 19, 1].”
A practical guide to Prabhakar fractional calculus (2020, unknown): “Luchko on the so-called multi-index Mittag–Leffler functions [83], [95], [84], [85].”
Some Applications of Mittag-Leffler Function in the Unit Disk (2016, unknown): “in [1], [2], [3], [4], [5], [7], [12], [13],[14], [15], [16], [19], [20] and [21].”
Multi-parametric mittag-leffler functions and their extension (2013, background): “Namely, in Kiryakova [31], [32] it was proved that functions (2.”
Asymptotics for a variant of the Mittag–Leffler function (2011, unknown): “If α is a natural number, then (1) is an instance of the multiple Mittag–Leffler function investigated by Yakubovich and Luchko [16] and Kiryakova [9], in connection with numerous applications to fractional calculus, but it seems that the asymptotic behaviour of the multiple Mittag–Leffler function ”
PATHWAY FRACTIONAL INTEGRATION OPERATOR (2009, background): “All rights reserved. as the hypergeometric integral operators of Saigo [17], the generalized fractional integrals involving G- and H-functions in Kiryakova [10], etc.”
On q–Analogues of Caputo Derivative and Mittag–Leffler Function (2007, methodology): “5] and [9], we can define the fractional q–integral and fractional q–derivative of any function, using the q-analogues of Mittag-Leffler functions as generating functions of some Gelfond-Leontiev (G-L) operators for generalized integration and differentiation.”
A Mittag-Leffler-type function of two variables (2013, methodology): “[7] Kiryakova V. Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus.”
Fractional-Order Derivatives and Integrals: Introductory Overview and Recent Developments (2020, background): “11) when γ = κ = 1 reduces to the following multi-index Mittag-Leffler function (see [33]; see also [16]):”