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Multivariate analogue of generalized Mittag-Leffler function
Integral Transforms and Special Functions, 2011Following the results of Saxena and Kalla [Solutions of Volterra-type integro-differential equations with a generalized Lauricella confluent hypergeometric function in the kernels, Int. J. Math. Math. Sci. 8 (2005), pp. 1155–1170], we introduce and develop here a theory of multivariate generalization of the Mittag-Leffler function, which is defined as:
R. K. Saxena, S. L. Kalla, Ravi Saxena
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Generalized mittag-leffler function and generalized fractional calculus operators
Integral Transforms and Special Functions, 2004The paper is devoted to the study of the function E γ ρ,μ(z) defined for complex ρ, μ, γ (Re(ρ) > 0) by which is a generalization of the classical Mittag-Leffler function E ρ,μ(z) and the Kummer confluent hypergeometric function Φ(γ, μ; z). The properties of E γ ρ,μ(z) including usual differentiation and integration, and fractional ones are proved ...
Anatoly A Kilbas, Megumi Saigo
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Dirichlet Averages of Generalized Mittag-Leffler Type Function
Fractal and Fractional, 2022 Since Gösta Magus Mittag-Leffler introduced the so-called Mittag-Leffler function in 1903 and studied its features in five subsequent notes, passing the first half of the 20th century during which the majority of scientists remained almost unaware ...
Dinesh Kumar +2 more
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On the Generalized Mittag-Leffler Function and its Application in a Fractional Telegraph Equation [PDF]
Mathematical Physics Analysis and Geometry, 2011 The classical Mittag-Leffler functions, involving one- and two-parameter, play an important role in the study of fractional-order differential (and integral) equations.
E Capelas De Oliveira +2 more
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Computers and Mathematics With Applications, 2010 Stability of fractional-order nonlinear dynamic systems is studied using Lyapunov direct method with the introductions of Mittag–Leffler stability and generalized Mittag–Leffler stability notions.
Yangquan Chen, Igor Podlubny
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On the generalized mittag-leffler type functions
Integral Transforms and Special Functions, 1998The paper is devoted to the study of the properties of the special functions generalizing the Mittag-Leffler type functions. The order and type of such entire functions are evaluated and recurrence relations are given. Connections with hypergeometric functions are discussed and differentiation formulae are proved.
R. Gorenflo, A.A. Kilbas, S.V. Rogosin
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Certain Integrals Involving Generalized Mittag-Leffler Functions
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Agarwal, P., Chand, M., Jain, Shilpi
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Fractional Integrations of a Generalized Mittag-Leffler Type Function and Its Application
Mathematics, 2019 A generalized form of the Mittag-Leffler function denoted by p E q ; δ λ , μ ; ν x is established and studied in this paper. The fractional integrals involving the newly defined function are investigated.
Kottakkaran Sooppy Nisar
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Overconvergence of Series in Generalized Mittag-Leffler Functions
Fractional Calculus and Applied Analysis, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Generalized Mittag-Leffler Factorial Function with Sums
2021This research aims to express several functions, like trigonometric functions, Mittag-Leffler (ML) function. For that we have introduced Generalized Mittag-Leffler function factorial by which one can express certain functions as well as series by sum of polynomial factorials.
Jaraldpushparaj Simon +1 more
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