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2010
This chapter is devoted to a brief summary of the most important properties of Mittag-Leffler functions. These functions play a fundamental role in many questions related to fractional differential equations, and they will be used frequently in the later chapters.
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This chapter is devoted to a brief summary of the most important properties of Mittag-Leffler functions. These functions play a fundamental role in many questions related to fractional differential equations, and they will be used frequently in the later chapters.
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Multi-index Mittag-Leffler Functions
2014Consider the function defined for \(\alpha _{1},\ \alpha _{2} \in \mathbb{R}\) (α 1 2 +α 2 2 ≠ 0) and \(\beta _{1},\beta _{2} \in \mathbb{C}\) by the series $$\displaystyle{ E_{\alpha _{1},\beta _{1};\alpha _{2},\beta _{2}}(z) \equiv \sum _{k=0}^{\infty } \frac{z^{k}} {\varGamma (\alpha _{1}k +\beta _{1})\varGamma (\alpha _{2}k +\beta _{2})}\ \ (z \
Rudolf Gorenflo +3 more
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When is a Mittag–Leffler function a Nussbaum function?
Automatica, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Li, Yan, Chen, Yangquan
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Mittag-Leffler type functions of three variables
Mathematical Methods in the Applied SciencesIn this article, we generalized Mittag-Leffler-type functions F~̵̄ A ( 3 ) , F~̵̄ B ( 3 ) , F~̵̄ C ( 3 ) and F~̵̄ D ( 3 ) , which correspond, respectively, to the familiar Lauricella hypergeometric functions F A ( 3 ) , F B ( 3 ) , F C ( 3 ) and F D ( 3 ) of three variables.
Anvar Hasanov, Hilola Yuldashova
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Generalized Fourier Multipliers via Mittag-Leffler Functions
Mediterranean Journal of MathematicsFourier multipliers have played an important role in harmonic analysis since from the outset. They play a decisive role in studying several integral operators such as singular integral operators, oscillatory integral operators, maximal functions, and Littlewood-Paley \(g\)-functions, among others.
Hawawsheh, Laith, Al-Salman, Ahmad
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Estimates for Integrals with Mittag-Leffler Functions
Lobachevskii Journal of MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ikromov, Isroil A., Safarov, Akbar R.
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Mittag-Leffler vector random fields with Mittag-Leffler direct and cross covariance functions
Annals of the Institute of Statistical Mathematics, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Mittag-leffler and related functions
Integral Transforms and Special Functions, 1993In our attempts to find solutions of fractional differential equations we are led, in a natural fashion, to the study of certain transcendental functions. These functions may be defined by a fractional integral or combinations of such integrals. Further investigations show that these new functions are intimately related to the classical Mittag-Leffler ...
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The Two-Parametric Mittag-Leffler Function
2014In this chapter we present the basic properties of the two-parametric Mittag-Leffler function E α, β (z) (see ( 1.0.3)), which is the most straightforward generalization of the classical Mittag-Leffler function E α (z) (see ( 3.1.1)).
Rudolf Gorenflo +3 more
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Mittag-Leffler Functions with Three Parameters
2014The Prabhakar generalized Mittag-Leffler function [Pra71] is defined as $$\displaystyle{ E_{\alpha,\beta }^{\gamma }(z):=\sum _{ n=0}^{\infty } \frac{(\gamma )_{n}} {n!\varGamma (\alpha n+\beta )}\,z^{n}\,,\quad Re\,(\alpha ) > 0,\,Re\,(\beta ) > 0,\,\gamma > 0, }$$ (5.1.1) where (γ) n = γ(γ + 1)…(γ + n − 1) (see formula (A.1.17)).
Rudolf Gorenflo +3 more
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